[{"data":1,"prerenderedAt":24608},["ShallowReactive",2],{"note:math\u002Fabstract_algebra\u002Fringhomomorphism":3,"site-search-catalogue":24607},{"id":4,"title":5,"body":6,"description":24590,"extension":24599,"meta":24600,"navigation":24602,"path":24603,"seo":24604,"stem":24605,"__hash__":24606},"notes\u002Fsource\u002Fmath\u002Fabstract_algebra\u002Fringhomomorphism.md","环同态基本定理",{"type":7,"value":8,"toc":24589},"minimark",[9,14,19,538,541,1600,1678,1985,1988,1992,2358,2363,2492,5214,5345,6549,7609,7611,7615,7849,8261,9071,9631,9800,10172,10509,10875,10980,14371,14373,14377,15561,15563,15567,15756,17144,17978,19465,20086,20121,22418],[10,11,13],"h1",{"id":12},"_33-同态基本定理-完整讲义版","3.3 同态基本定理 (完整讲义版)",[15,16,18],"h3",{"id":17},"_1-环同态的定义与分类","1. 环同态的定义与分类",[20,21,22,26,27,95,96,176,177,251,252,503,504,533,534,537],"p",{},[23,24,25],"strong",{},"定义 3.3.1."," 设 ",[28,29,32,63],"span",{"className":30},[31],"katex",[28,33,36],{"className":34},[35],"katex-mathml",[37,38,40],"math",{"xmlns":39},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[41,42,43,58],"semantics",{},[44,45,46,50,55],"mrow",{},[47,48,49],"mi",{},"R",[51,52,54],"mo",{"separator":53},"true",",",[47,56,57],{},"S",[59,60,62],"annotation",{"encoding":61},"application\u002Fx-tex","R, S",[28,64,67],{"className":65,"ariaHidden":53},[66],"katex-html",[28,68,71,76,82,86,91],{"className":69},[70],"base",[28,72],{"className":73,"style":75},[74],"strut","height:0.8778em;vertical-align:-0.1944em;",[28,77,49],{"className":78,"style":81},[79,80],"mord","mathnormal","margin-right:0.0077em;",[28,83,54],{"className":84},[85],"mpunct",[28,87],{"className":88,"style":90},[89],"mspace","margin-right:0.1667em;",[28,92,57],{"className":93,"style":94},[79,80],"margin-right:0.0576em;"," 是两个环。如果映射 ",[28,97,99,124],{"className":98},[31],[28,100,102],{"className":101},[35],[37,103,104],{"xmlns":39},[41,105,106,121],{},[44,107,108,111,114,116,119],{},[47,109,110],{},"ϕ",[51,112,113],{},":",[47,115,49],{},[51,117,118],{},"→",[47,120,57],{},[59,122,123],{"encoding":61},"\\phi: R \\to S",[28,125,127,148,167],{"className":126,"ariaHidden":53},[66],[28,128,130,134,137,141,145],{"className":129},[70],[28,131],{"className":132,"style":133},[74],"height:0.8889em;vertical-align:-0.1944em;",[28,135,110],{"className":136},[79,80],[28,138],{"className":139,"style":140},[89],"margin-right:0.2778em;",[28,142,113],{"className":143},[144],"mrel",[28,146],{"className":147,"style":140},[89],[28,149,151,155,158,161,164],{"className":150},[70],[28,152],{"className":153,"style":154},[74],"height:0.6833em;",[28,156,49],{"className":157,"style":81},[79,80],[28,159],{"className":160,"style":140},[89],[28,162,118],{"className":163},[144],[28,165],{"className":166,"style":140},[89],[28,168,170,173],{"className":169},[70],[28,171],{"className":172,"style":154},[74],[28,174,57],{"className":175,"style":94},[79,80]," 满足 ",[28,178,180,209],{"className":179},[31],[28,181,183],{"className":182},[35],[37,184,185],{"xmlns":39},[41,186,187,206],{},[44,188,189,193,196,198,201,204],{},[47,190,192],{"mathvariant":191},"normal","∀",[47,194,195],{},"a",[51,197,54],{"separator":53},[47,199,200],{},"b",[51,202,203],{},"∈",[47,205,49],{},[59,207,208],{"encoding":61},"\\forall a, b \\in R",[28,210,212,242],{"className":211,"ariaHidden":53},[66],[28,213,215,218,221,224,227,230,233,236,239],{"className":214},[70],[28,216],{"className":217,"style":133},[74],[28,219,192],{"className":220},[79],[28,222,195],{"className":223},[79,80],[28,225,54],{"className":226},[85],[28,228],{"className":229,"style":90},[89],[28,231,200],{"className":232},[79,80],[28,234],{"className":235,"style":140},[89],[28,237,203],{"className":238},[144],[28,240],{"className":241,"style":140},[89],[28,243,245,248],{"className":244},[70],[28,246],{"className":247,"style":154},[74],[28,249,49],{"className":250,"style":81},[79,80],"，都有\n",[28,253,255,340],{"className":254},[31],[28,256,258],{"className":257},[35],[37,259,260],{"xmlns":39},[41,261,262,337],{},[44,263,264,266,270,272,275,277,280,283,285,287,289,291,293,295,297,299,301,303,306,308,310,312,314,316,318,320,322,324,326,328,330,332,334],{},[47,265,110],{},[51,267,269],{"stretchy":268},"false","(",[47,271,195],{},[51,273,274],{},"+",[47,276,200],{},[51,278,279],{"stretchy":268},")",[51,281,282],{},"=",[47,284,110],{},[51,286,269],{"stretchy":268},[47,288,195],{},[51,290,279],{"stretchy":268},[51,292,274],{},[47,294,110],{},[51,296,269],{"stretchy":268},[47,298,200],{},[51,300,279],{"stretchy":268},[51,302,54],{"separator":53},[89,304],{"width":305},"1em",[47,307,110],{},[51,309,269],{"stretchy":268},[47,311,195],{},[47,313,200],{},[51,315,279],{"stretchy":268},[51,317,282],{},[47,319,110],{},[51,321,269],{"stretchy":268},[47,323,195],{},[51,325,279],{"stretchy":268},[47,327,110],{},[51,329,269],{"stretchy":268},[47,331,200],{},[51,333,279],{"stretchy":268},[47,335,336],{"mathvariant":191},".",[59,338,339],{"encoding":61},"\\phi(a+b) = \\phi(a) + \\phi(b), \\quad \\phi(ab) = \\phi(a)\\phi(b).",[28,341,343,371,393,420,470],{"className":342,"ariaHidden":53},[66],[28,344,346,350,353,357,360,364,368],{"className":345},[70],[28,347],{"className":348,"style":349},[74],"height:1em;vertical-align:-0.25em;",[28,351,110],{"className":352},[79,80],[28,354,269],{"className":355},[356],"mopen",[28,358,195],{"className":359},[79,80],[28,361],{"className":362,"style":363},[89],"margin-right:0.2222em;",[28,365,274],{"className":366},[367],"mbin",[28,369],{"className":370,"style":363},[89],[28,372,374,377,380,384,387,390],{"className":373},[70],[28,375],{"className":376,"style":349},[74],[28,378,200],{"className":379},[79,80],[28,381,279],{"className":382},[383],"mclose",[28,385],{"className":386,"style":140},[89],[28,388,282],{"className":389},[144],[28,391],{"className":392,"style":140},[89],[28,394,396,399,402,405,408,411,414,417],{"className":395},[70],[28,397],{"className":398,"style":349},[74],[28,400,110],{"className":401},[79,80],[28,403,269],{"className":404},[356],[28,406,195],{"className":407},[79,80],[28,409,279],{"className":410},[383],[28,412],{"className":413,"style":363},[89],[28,415,274],{"className":416},[367],[28,418],{"className":419,"style":363},[89],[28,421,423,426,429,432,435,438,441,445,448,451,454,458,461,464,467],{"className":422},[70],[28,424],{"className":425,"style":349},[74],[28,427,110],{"className":428},[79,80],[28,430,269],{"className":431},[356],[28,433,200],{"className":434},[79,80],[28,436,279],{"className":437},[383],[28,439,54],{"className":440},[85],[28,442],{"className":443,"style":444},[89],"margin-right:1em;",[28,446],{"className":447,"style":90},[89],[28,449,110],{"className":450},[79,80],[28,452,269],{"className":453},[356],[28,455,457],{"className":456},[79,80],"ab",[28,459,279],{"className":460},[383],[28,462],{"className":463,"style":140},[89],[28,465,282],{"className":466},[144],[28,468],{"className":469,"style":140},[89],[28,471,473,476,479,482,485,488,491,494,497,500],{"className":472},[70],[28,474],{"className":475,"style":349},[74],[28,477,110],{"className":478},[79,80],[28,480,269],{"className":481},[356],[28,483,195],{"className":484},[79,80],[28,486,279],{"className":487},[383],[28,489,110],{"className":490},[79,80],[28,492,269],{"className":493},[356],[28,495,200],{"className":496},[79,80],[28,498,279],{"className":499},[383],[28,501,336],{"className":502},[79],"\n则称 ",[28,505,507,521],{"className":506},[31],[28,508,510],{"className":509},[35],[37,511,512],{"xmlns":39},[41,513,514,518],{},[44,515,516],{},[47,517,110],{},[59,519,520],{"encoding":61},"\\phi",[28,522,524],{"className":523,"ariaHidden":53},[66],[28,525,527,530],{"className":526},[70],[28,528],{"className":529,"style":133},[74],[28,531,110],{"className":532},[79,80]," 是一个",[23,535,536],{},"环同态","。",[20,539,540],{},"在此基础上，我们补充以下具体的同态分类定义（原文省略部分）：",[542,543,544,814,1045,1202,1399],"ol",{},[545,546,547,550,551,579,580,648,649,730,731,784,785,813],"li",{},[23,548,549],{},"单同态 (Monomorphism)",": 若 ",[28,552,554,567],{"className":553},[31],[28,555,557],{"className":556},[35],[37,558,559],{"xmlns":39},[41,560,561,565],{},[44,562,563],{},[47,564,110],{},[59,566,520],{"encoding":61},[28,568,570],{"className":569,"ariaHidden":53},[66],[28,571,573,576],{"className":572},[70],[28,574],{"className":575,"style":133},[74],[28,577,110],{"className":578},[79,80]," 是单射（即 ",[28,581,583,606],{"className":582},[31],[28,584,586],{"className":585},[35],[37,587,588],{"xmlns":39},[41,589,590,604],{},[44,591,592,594,596,598,600,602],{},[47,593,192],{"mathvariant":191},[47,595,195],{},[51,597,54],{"separator":53},[47,599,200],{},[51,601,203],{},[47,603,49],{},[59,605,208],{"encoding":61},[28,607,609,639],{"className":608,"ariaHidden":53},[66],[28,610,612,615,618,621,624,627,630,633,636],{"className":611},[70],[28,613],{"className":614,"style":133},[74],[28,616,192],{"className":617},[79],[28,619,195],{"className":620},[79,80],[28,622,54],{"className":623},[85],[28,625],{"className":626,"style":90},[89],[28,628,200],{"className":629},[79,80],[28,631],{"className":632,"style":140},[89],[28,634,203],{"className":635},[144],[28,637],{"className":638,"style":140},[89],[28,640,642,645],{"className":641},[70],[28,643],{"className":644,"style":154},[74],[28,646,49],{"className":647,"style":81},[79,80],"，若 ",[28,650,652,682],{"className":651},[31],[28,653,655],{"className":654},[35],[37,656,657],{"xmlns":39},[41,658,659,679],{},[44,660,661,663,665,667,669,671,673,675,677],{},[47,662,110],{},[51,664,269],{"stretchy":268},[47,666,195],{},[51,668,279],{"stretchy":268},[51,670,282],{},[47,672,110],{},[51,674,269],{"stretchy":268},[47,676,200],{},[51,678,279],{"stretchy":268},[59,680,681],{"encoding":61},"\\phi(a) = \\phi(b)",[28,683,685,712],{"className":684,"ariaHidden":53},[66],[28,686,688,691,694,697,700,703,706,709],{"className":687},[70],[28,689],{"className":690,"style":349},[74],[28,692,110],{"className":693},[79,80],[28,695,269],{"className":696},[356],[28,698,195],{"className":699},[79,80],[28,701,279],{"className":702},[383],[28,704],{"className":705,"style":140},[89],[28,707,282],{"className":708},[144],[28,710],{"className":711,"style":140},[89],[28,713,715,718,721,724,727],{"className":714},[70],[28,716],{"className":717,"style":349},[74],[28,719,110],{"className":720},[79,80],[28,722,269],{"className":723},[356],[28,725,200],{"className":726},[79,80],[28,728,279],{"className":729},[383]," 则 ",[28,732,734,752],{"className":733},[31],[28,735,737],{"className":736},[35],[37,738,739],{"xmlns":39},[41,740,741,749],{},[44,742,743,745,747],{},[47,744,195],{},[51,746,282],{},[47,748,200],{},[59,750,751],{"encoding":61},"a=b",[28,753,755,774],{"className":754,"ariaHidden":53},[66],[28,756,758,762,765,768,771],{"className":757},[70],[28,759],{"className":760,"style":761},[74],"height:0.4306em;",[28,763,195],{"className":764},[79,80],[28,766],{"className":767,"style":140},[89],[28,769,282],{"className":770},[144],[28,772],{"className":773,"style":140},[89],[28,775,777,781],{"className":776},[70],[28,778],{"className":779,"style":780},[74],"height:0.6944em;",[28,782,200],{"className":783},[79,80],"），称 ",[28,786,788,801],{"className":787},[31],[28,789,791],{"className":790},[35],[37,792,793],{"xmlns":39},[41,794,795,799],{},[44,796,797],{},[47,798,110],{},[59,800,520],{"encoding":61},[28,802,804],{"className":803,"ariaHidden":53},[66],[28,805,807,810],{"className":806},[70],[28,808],{"className":809,"style":133},[74],[28,811,110],{"className":812},[79,80]," 为单同态。",[545,815,816,550,819,847,848,949,950,784,1016,1044],{},[23,817,818],{},"满同态 (Epimorphism)",[28,820,822,835],{"className":821},[31],[28,823,825],{"className":824},[35],[37,826,827],{"xmlns":39},[41,828,829,833],{},[44,830,831],{},[47,832,110],{},[59,834,520],{"encoding":61},[28,836,838],{"className":837,"ariaHidden":53},[66],[28,839,841,844],{"className":840},[70],[28,842],{"className":843,"style":133},[74],[28,845,110],{"className":846},[79,80]," 是满射（即 ",[28,849,851,884],{"className":850},[31],[28,852,854],{"className":853},[35],[37,855,856],{"xmlns":39},[41,857,858,881],{},[44,859,860,862,865,867,869,871,874,877,879],{},[47,861,192],{"mathvariant":191},[47,863,864],{},"s",[51,866,203],{},[47,868,57],{},[51,870,54],{"separator":53},[47,872,873],{"mathvariant":191},"∃",[47,875,876],{},"r",[51,878,203],{},[47,880,49],{},[59,882,883],{"encoding":61},"\\forall s \\in S, \\exists r \\in R",[28,885,887,909,940],{"className":886,"ariaHidden":53},[66],[28,888,890,894,897,900,903,906],{"className":889},[70],[28,891],{"className":892,"style":893},[74],"height:0.7335em;vertical-align:-0.0391em;",[28,895,192],{"className":896},[79],[28,898,864],{"className":899},[79,80],[28,901],{"className":902,"style":140},[89],[28,904,203],{"className":905},[144],[28,907],{"className":908,"style":140},[89],[28,910,912,915,918,921,924,927,931,934,937],{"className":911},[70],[28,913],{"className":914,"style":133},[74],[28,916,57],{"className":917,"style":94},[79,80],[28,919,54],{"className":920},[85],[28,922],{"className":923,"style":90},[89],[28,925,873],{"className":926},[79],[28,928,876],{"className":929,"style":930},[79,80],"margin-right:0.0278em;",[28,932],{"className":933,"style":140},[89],[28,935,203],{"className":936},[144],[28,938],{"className":939,"style":140},[89],[28,941,943,946],{"className":942},[70],[28,944],{"className":945,"style":154},[74],[28,947,49],{"className":948,"style":81},[79,80]," 使得 ",[28,951,953,977],{"className":952},[31],[28,954,956],{"className":955},[35],[37,957,958],{"xmlns":39},[41,959,960,974],{},[44,961,962,964,966,968,970,972],{},[47,963,110],{},[51,965,269],{"stretchy":268},[47,967,876],{},[51,969,279],{"stretchy":268},[51,971,282],{},[47,973,864],{},[59,975,976],{"encoding":61},"\\phi(r)=s",[28,978,980,1007],{"className":979,"ariaHidden":53},[66],[28,981,983,986,989,992,995,998,1001,1004],{"className":982},[70],[28,984],{"className":985,"style":349},[74],[28,987,110],{"className":988},[79,80],[28,990,269],{"className":991},[356],[28,993,876],{"className":994,"style":930},[79,80],[28,996,279],{"className":997},[383],[28,999],{"className":1000,"style":140},[89],[28,1002,282],{"className":1003},[144],[28,1005],{"className":1006,"style":140},[89],[28,1008,1010,1013],{"className":1009},[70],[28,1011],{"className":1012,"style":761},[74],[28,1014,864],{"className":1015},[79,80],[28,1017,1019,1032],{"className":1018},[31],[28,1020,1022],{"className":1021},[35],[37,1023,1024],{"xmlns":39},[41,1025,1026,1030],{},[44,1027,1028],{},[47,1029,110],{},[59,1031,520],{"encoding":61},[28,1033,1035],{"className":1034,"ariaHidden":53},[66],[28,1036,1038,1041],{"className":1037},[70],[28,1039],{"className":1040,"style":133},[74],[28,1042,110],{"className":1043},[79,80]," 为满同态。",[545,1046,1047,550,1050,1078,1079,1107,1108,1149,1150,537],{},[23,1048,1049],{},"同构 (Isomorphism)",[28,1051,1053,1066],{"className":1052},[31],[28,1054,1056],{"className":1055},[35],[37,1057,1058],{"xmlns":39},[41,1059,1060,1064],{},[44,1061,1062],{},[47,1063,110],{},[59,1065,520],{"encoding":61},[28,1067,1069],{"className":1068,"ariaHidden":53},[66],[28,1070,1072,1075],{"className":1071},[70],[28,1073],{"className":1074,"style":133},[74],[28,1076,110],{"className":1077},[79,80]," 既是单射又是满射（即双射），称 ",[28,1080,1082,1095],{"className":1081},[31],[28,1083,1085],{"className":1084},[35],[37,1086,1087],{"xmlns":39},[41,1088,1089,1093],{},[44,1090,1091],{},[47,1092,110],{},[59,1094,520],{"encoding":61},[28,1096,1098],{"className":1097,"ariaHidden":53},[66],[28,1099,1101,1104],{"className":1100},[70],[28,1102],{"className":1103,"style":133},[74],[28,1105,110],{"className":1106},[79,80]," 为同构。若 ",[28,1109,1111,1128],{"className":1110},[31],[28,1112,1114],{"className":1113},[35],[37,1115,1116],{"xmlns":39},[41,1117,1118,1126],{},[44,1119,1120,1122,1124],{},[47,1121,49],{},[51,1123,54],{"separator":53},[47,1125,57],{},[59,1127,62],{"encoding":61},[28,1129,1131],{"className":1130,"ariaHidden":53},[66],[28,1132,1134,1137,1140,1143,1146],{"className":1133},[70],[28,1135],{"className":1136,"style":75},[74],[28,1138,49],{"className":1139,"style":81},[79,80],[28,1141,54],{"className":1142},[85],[28,1144],{"className":1145,"style":90},[89],[28,1147,57],{"className":1148,"style":94},[79,80]," 之间存在同构，记为 ",[28,1151,1153,1172],{"className":1152},[31],[28,1154,1156],{"className":1155},[35],[37,1157,1158],{"xmlns":39},[41,1159,1160,1169],{},[44,1161,1162,1164,1167],{},[47,1163,49],{},[51,1165,1166],{},"≅",[47,1168,57],{},[59,1170,1171],{"encoding":61},"R \\cong S",[28,1173,1175,1193],{"className":1174,"ariaHidden":53},[66],[28,1176,1178,1181,1184,1187,1190],{"className":1177},[70],[28,1179],{"className":1180,"style":154},[74],[28,1182,49],{"className":1183,"style":81},[79,80],[28,1185],{"className":1186,"style":140},[89],[28,1188,1166],{"className":1189},[144],[28,1191],{"className":1192,"style":140},[89],[28,1194,1196,1199],{"className":1195},[70],[28,1197],{"className":1198,"style":154},[74],[28,1200,57],{"className":1201,"style":94},[79,80],[545,1203,1204,550,1207,1258,1259,1287,1288,1316,1317,1345,1346,537],{},[23,1205,1206],{},"自同态 (Endomorphism)",[28,1208,1210,1228],{"className":1209},[31],[28,1211,1213],{"className":1212},[35],[37,1214,1215],{"xmlns":39},[41,1216,1217,1225],{},[44,1218,1219,1221,1223],{},[47,1220,57],{},[51,1222,282],{},[47,1224,49],{},[59,1226,1227],{"encoding":61},"S=R",[28,1229,1231,1249],{"className":1230,"ariaHidden":53},[66],[28,1232,1234,1237,1240,1243,1246],{"className":1233},[70],[28,1235],{"className":1236,"style":154},[74],[28,1238,57],{"className":1239,"style":94},[79,80],[28,1241],{"className":1242,"style":140},[89],[28,1244,282],{"className":1245},[144],[28,1247],{"className":1248,"style":140},[89],[28,1250,1252,1255],{"className":1251},[70],[28,1253],{"className":1254,"style":154},[74],[28,1256,49],{"className":1257,"style":81},[79,80],"，即从环 ",[28,1260,1262,1275],{"className":1261},[31],[28,1263,1265],{"className":1264},[35],[37,1266,1267],{"xmlns":39},[41,1268,1269,1273],{},[44,1270,1271],{},[47,1272,49],{},[59,1274,49],{"encoding":61},[28,1276,1278],{"className":1277,"ariaHidden":53},[66],[28,1279,1281,1284],{"className":1280},[70],[28,1282],{"className":1283,"style":154},[74],[28,1285,49],{"className":1286,"style":81},[79,80]," 到自身的同态，称 ",[28,1289,1291,1304],{"className":1290},[31],[28,1292,1294],{"className":1293},[35],[37,1295,1296],{"xmlns":39},[41,1297,1298,1302],{},[44,1299,1300],{},[47,1301,110],{},[59,1303,520],{"encoding":61},[28,1305,1307],{"className":1306,"ariaHidden":53},[66],[28,1308,1310,1313],{"className":1309},[70],[28,1311],{"className":1312,"style":133},[74],[28,1314,110],{"className":1315},[79,80]," 为自同态。所有 ",[28,1318,1320,1333],{"className":1319},[31],[28,1321,1323],{"className":1322},[35],[37,1324,1325],{"xmlns":39},[41,1326,1327,1331],{},[44,1328,1329],{},[47,1330,49],{},[59,1332,49],{"encoding":61},[28,1334,1336],{"className":1335,"ariaHidden":53},[66],[28,1337,1339,1342],{"className":1338},[70],[28,1340],{"className":1341,"style":154},[74],[28,1343,49],{"className":1344,"style":81},[79,80]," 的自同态构成的集合记为 ",[28,1347,1349,1373],{"className":1348},[31],[28,1350,1352],{"className":1351},[35],[37,1353,1354],{"xmlns":39},[41,1355,1356,1370],{},[44,1357,1358,1361,1364,1366,1368],{},[47,1359,1360],{"mathvariant":191},"End",[51,1362,1363],{},"⁡",[51,1365,269],{"stretchy":268},[47,1367,49],{},[51,1369,279],{"stretchy":268},[59,1371,1372],{"encoding":61},"\\operatorname{End}(R)",[28,1374,1376],{"className":1375,"ariaHidden":53},[66],[28,1377,1379,1382,1390,1393,1396],{"className":1378},[70],[28,1380],{"className":1381,"style":349},[74],[28,1383,1386],{"className":1384},[1385],"mop",[28,1387,1360],{"className":1388},[79,1389],"mathrm",[28,1391,269],{"className":1392},[356],[28,1394,49],{"className":1395,"style":81},[79,80],[28,1397,279],{"className":1398},[383],[545,1400,1401,550,1404,1432,1433,1461,1462,1490,1491,1519,1520,1548,1549,1599],{},[23,1402,1403],{},"自同构 (Automorphism)",[28,1405,1407,1420],{"className":1406},[31],[28,1408,1410],{"className":1409},[35],[37,1411,1412],{"xmlns":39},[41,1413,1414,1418],{},[44,1415,1416],{},[47,1417,110],{},[59,1419,520],{"encoding":61},[28,1421,1423],{"className":1422,"ariaHidden":53},[66],[28,1424,1426,1429],{"className":1425},[70],[28,1427],{"className":1428,"style":133},[74],[28,1430,110],{"className":1431},[79,80]," 是 ",[28,1434,1436,1449],{"className":1435},[31],[28,1437,1439],{"className":1438},[35],[37,1440,1441],{"xmlns":39},[41,1442,1443,1447],{},[44,1444,1445],{},[47,1446,49],{},[59,1448,49],{"encoding":61},[28,1450,1452],{"className":1451,"ariaHidden":53},[66],[28,1453,1455,1458],{"className":1454},[70],[28,1456],{"className":1457,"style":154},[74],[28,1459,49],{"className":1460,"style":81},[79,80]," 到 ",[28,1463,1465,1478],{"className":1464},[31],[28,1466,1468],{"className":1467},[35],[37,1469,1470],{"xmlns":39},[41,1471,1472,1476],{},[44,1473,1474],{},[47,1475,49],{},[59,1477,49],{"encoding":61},[28,1479,1481],{"className":1480,"ariaHidden":53},[66],[28,1482,1484,1487],{"className":1483},[70],[28,1485],{"className":1486,"style":154},[74],[28,1488,49],{"className":1489,"style":81},[79,80]," 的同构，称 ",[28,1492,1494,1507],{"className":1493},[31],[28,1495,1497],{"className":1496},[35],[37,1498,1499],{"xmlns":39},[41,1500,1501,1505],{},[44,1502,1503],{},[47,1504,110],{},[59,1506,520],{"encoding":61},[28,1508,1510],{"className":1509,"ariaHidden":53},[66],[28,1511,1513,1516],{"className":1512},[70],[28,1514],{"className":1515,"style":133},[74],[28,1517,110],{"className":1518},[79,80]," 为自同构。所有 ",[28,1521,1523,1536],{"className":1522},[31],[28,1524,1526],{"className":1525},[35],[37,1527,1528],{"xmlns":39},[41,1529,1530,1534],{},[44,1531,1532],{},[47,1533,49],{},[59,1535,49],{"encoding":61},[28,1537,1539],{"className":1538,"ariaHidden":53},[66],[28,1540,1542,1545],{"className":1541},[70],[28,1543],{"className":1544,"style":154},[74],[28,1546,49],{"className":1547,"style":81},[79,80]," 的自同构构成的集合记为 ",[28,1550,1552,1575],{"className":1551},[31],[28,1553,1555],{"className":1554},[35],[37,1556,1557],{"xmlns":39},[41,1558,1559,1572],{},[44,1560,1561,1564,1566,1568,1570],{},[47,1562,1563],{"mathvariant":191},"Aut",[51,1565,1363],{},[51,1567,269],{"stretchy":268},[47,1569,49],{},[51,1571,279],{"stretchy":268},[59,1573,1574],{"encoding":61},"\\operatorname{Aut}(R)",[28,1576,1578],{"className":1577,"ariaHidden":53},[66],[28,1579,1581,1584,1590,1593,1596],{"className":1580},[70],[28,1582],{"className":1583,"style":349},[74],[28,1585,1587],{"className":1586},[1385],[28,1588,1563],{"className":1589},[79,1389],[28,1591,269],{"className":1592},[356],[28,1594,49],{"className":1595,"style":81},[79,80],[28,1597,279],{"className":1598},[383],"（它关于映射复合构成一个群）。",[20,1601,1602,26,1605,1677],{},[23,1603,1604],{},"定义.",[28,1606,1608,1629],{"className":1607},[31],[28,1609,1611],{"className":1610},[35],[37,1612,1613],{"xmlns":39},[41,1614,1615,1627],{},[44,1616,1617,1619,1621,1623,1625],{},[47,1618,110],{},[51,1620,113],{},[47,1622,49],{},[51,1624,118],{},[47,1626,57],{},[59,1628,123],{"encoding":61},[28,1630,1632,1650,1668],{"className":1631,"ariaHidden":53},[66],[28,1633,1635,1638,1641,1644,1647],{"className":1634},[70],[28,1636],{"className":1637,"style":133},[74],[28,1639,110],{"className":1640},[79,80],[28,1642],{"className":1643,"style":140},[89],[28,1645,113],{"className":1646},[144],[28,1648],{"className":1649,"style":140},[89],[28,1651,1653,1656,1659,1662,1665],{"className":1652},[70],[28,1654],{"className":1655,"style":154},[74],[28,1657,49],{"className":1658,"style":81},[79,80],[28,1660],{"className":1661,"style":140},[89],[28,1663,118],{"className":1664},[144],[28,1666],{"className":1667,"style":140},[89],[28,1669,1671,1674],{"className":1670},[70],[28,1672],{"className":1673,"style":154},[74],[28,1675,57],{"className":1676,"style":94},[79,80]," 是环同态。",[1679,1680,1681,1845],"ul",{},[545,1682,1683,1686,1687,537],{},[23,1684,1685],{},"核 (Kernel)",": ",[28,1688,1690,1740],{"className":1689},[31],[28,1691,1693],{"className":1692},[35],[37,1694,1695],{"xmlns":39},[41,1696,1697,1737],{},[44,1698,1699,1702,1704,1706,1708,1711,1713,1715,1717,1720,1722,1724,1726,1728,1730,1734],{},[47,1700,1701],{},"ker",[51,1703,1363],{},[47,1705,110],{},[51,1707,282],{},[51,1709,1710],{"stretchy":268},"{",[47,1712,195],{},[51,1714,203],{},[47,1716,49],{},[51,1718,1719],{},"∣",[47,1721,110],{},[51,1723,269],{"stretchy":268},[47,1725,195],{},[51,1727,279],{"stretchy":268},[51,1729,282],{},[1731,1732,1733],"mn",{},"0",[51,1735,1736],{"stretchy":268},"}",[59,1738,1739],{"encoding":61},"\\ker \\phi = \\{a \\in R \\mid \\phi(a) = 0\\}",[28,1741,1743,1767,1788,1806,1833],{"className":1742,"ariaHidden":53},[66],[28,1744,1746,1749,1752,1755,1758,1761,1764],{"className":1745},[70],[28,1747],{"className":1748,"style":133},[74],[28,1750,1701],{"className":1751},[1385],[28,1753],{"className":1754,"style":90},[89],[28,1756,110],{"className":1757},[79,80],[28,1759],{"className":1760,"style":140},[89],[28,1762,282],{"className":1763},[144],[28,1765],{"className":1766,"style":140},[89],[28,1768,1770,1773,1776,1779,1782,1785],{"className":1769},[70],[28,1771],{"className":1772,"style":349},[74],[28,1774,1710],{"className":1775},[356],[28,1777,195],{"className":1778},[79,80],[28,1780],{"className":1781,"style":140},[89],[28,1783,203],{"className":1784},[144],[28,1786],{"className":1787,"style":140},[89],[28,1789,1791,1794,1797,1800,1803],{"className":1790},[70],[28,1792],{"className":1793,"style":349},[74],[28,1795,49],{"className":1796,"style":81},[79,80],[28,1798],{"className":1799,"style":140},[89],[28,1801,1719],{"className":1802},[144],[28,1804],{"className":1805,"style":140},[89],[28,1807,1809,1812,1815,1818,1821,1824,1827,1830],{"className":1808},[70],[28,1810],{"className":1811,"style":349},[74],[28,1813,110],{"className":1814},[79,80],[28,1816,269],{"className":1817},[356],[28,1819,195],{"className":1820},[79,80],[28,1822,279],{"className":1823},[383],[28,1825],{"className":1826,"style":140},[89],[28,1828,282],{"className":1829},[144],[28,1831],{"className":1832,"style":140},[89],[28,1834,1836,1839,1842],{"className":1835},[70],[28,1837],{"className":1838,"style":349},[74],[28,1840,1733],{"className":1841},[79],[28,1843,1736],{"className":1844},[383],[545,1846,1847,1686,1850,537],{},[23,1848,1849],{},"像 (Image)",[28,1851,1853,1894],{"className":1852},[31],[28,1854,1856],{"className":1855},[35],[37,1857,1858],{"xmlns":39},[41,1859,1860,1891],{},[44,1861,1862,1865,1867,1869,1871,1873,1875,1877,1879,1881,1883,1885,1887,1889],{},[47,1863,1864],{"mathvariant":191},"Im",[51,1866,1363],{},[47,1868,110],{},[51,1870,282],{},[51,1872,1710],{"stretchy":268},[47,1874,110],{},[51,1876,269],{"stretchy":268},[47,1878,195],{},[51,1880,279],{"stretchy":268},[51,1882,1719],{},[47,1884,195],{},[51,1886,203],{},[47,1888,49],{},[51,1890,1736],{"stretchy":268},[59,1892,1893],{"encoding":61},"\\operatorname{Im} \\phi = \\{\\phi(a) \\mid a \\in R\\}",[28,1895,1897,1924,1954,1973],{"className":1896,"ariaHidden":53},[66],[28,1898,1900,1903,1909,1912,1915,1918,1921],{"className":1899},[70],[28,1901],{"className":1902,"style":133},[74],[28,1904,1906],{"className":1905},[1385],[28,1907,1864],{"className":1908},[79,1389],[28,1910],{"className":1911,"style":90},[89],[28,1913,110],{"className":1914},[79,80],[28,1916],{"className":1917,"style":140},[89],[28,1919,282],{"className":1920},[144],[28,1922],{"className":1923,"style":140},[89],[28,1925,1927,1930,1933,1936,1939,1942,1945,1948,1951],{"className":1926},[70],[28,1928],{"className":1929,"style":349},[74],[28,1931,1710],{"className":1932},[356],[28,1934,110],{"className":1935},[79,80],[28,1937,269],{"className":1938},[356],[28,1940,195],{"className":1941},[79,80],[28,1943,279],{"className":1944},[383],[28,1946],{"className":1947,"style":140},[89],[28,1949,1719],{"className":1950},[144],[28,1952],{"className":1953,"style":140},[89],[28,1955,1957,1961,1964,1967,1970],{"className":1956},[70],[28,1958],{"className":1959,"style":1960},[74],"height:0.5782em;vertical-align:-0.0391em;",[28,1962,195],{"className":1963},[79,80],[28,1965],{"className":1966,"style":140},[89],[28,1968,203],{"className":1969},[144],[28,1971],{"className":1972,"style":140},[89],[28,1974,1976,1979,1982],{"className":1975},[70],[28,1977],{"className":1978,"style":349},[74],[28,1980,49],{"className":1981,"style":81},[79,80],[28,1983,1736],{"className":1984},[383],[1986,1987],"hr",{},[15,1989,1991],{"id":1990},"_2-同态的基本性质","2. 同态的基本性质",[20,1993,1994,26,1997,2069,2070,2133,2134,2162,2163,2228,2229,2257,2258,2286,2287,336],{},[23,1995,1996],{},"命题 3.3.1.",[28,1998,2000,2021],{"className":1999},[31],[28,2001,2003],{"className":2002},[35],[37,2004,2005],{"xmlns":39},[41,2006,2007,2019],{},[44,2008,2009,2011,2013,2015,2017],{},[47,2010,110],{},[51,2012,113],{},[47,2014,49],{},[51,2016,118],{},[47,2018,57],{},[59,2020,123],{"encoding":61},[28,2022,2024,2042,2060],{"className":2023,"ariaHidden":53},[66],[28,2025,2027,2030,2033,2036,2039],{"className":2026},[70],[28,2028],{"className":2029,"style":133},[74],[28,2031,110],{"className":2032},[79,80],[28,2034],{"className":2035,"style":140},[89],[28,2037,113],{"className":2038},[144],[28,2040],{"className":2041,"style":140},[89],[28,2043,2045,2048,2051,2054,2057],{"className":2044},[70],[28,2046],{"className":2047,"style":154},[74],[28,2049,49],{"className":2050,"style":81},[79,80],[28,2052],{"className":2053,"style":140},[89],[28,2055,118],{"className":2056},[144],[28,2058],{"className":2059,"style":140},[89],[28,2061,2063,2066],{"className":2062},[70],[28,2064],{"className":2065,"style":154},[74],[28,2067,57],{"className":2068,"style":94},[79,80]," 是一个环同态。\n(i) ",[28,2071,2073,2096],{"className":2072},[31],[28,2074,2076],{"className":2075},[35],[37,2077,2078],{"xmlns":39},[41,2079,2080,2093],{},[44,2081,2082,2084,2086,2088,2091],{},[47,2083,1701],{},[51,2085,1363],{},[47,2087,110],{},[51,2089,2090],{},"⊲",[47,2092,49],{},[59,2094,2095],{"encoding":61},"\\ker \\phi \\lhd R",[28,2097,2099,2124],{"className":2098,"ariaHidden":53},[66],[28,2100,2102,2105,2108,2111,2114,2117,2121],{"className":2101},[70],[28,2103],{"className":2104,"style":133},[74],[28,2106,1701],{"className":2107},[1385],[28,2109],{"className":2110,"style":90},[89],[28,2112,110],{"className":2113},[79,80],[28,2115],{"className":2116,"style":363},[89],[28,2118,2090],{"className":2119},[367,2120],"amsrm",[28,2122],{"className":2123,"style":363},[89],[28,2125,2127,2130],{"className":2126},[70],[28,2128],{"className":2129,"style":154},[74],[28,2131,49],{"className":2132,"style":81},[79,80]," (核是 ",[28,2135,2137,2150],{"className":2136},[31],[28,2138,2140],{"className":2139},[35],[37,2141,2142],{"xmlns":39},[41,2143,2144,2148],{},[44,2145,2146],{},[47,2147,49],{},[59,2149,49],{"encoding":61},[28,2151,2153],{"className":2152,"ariaHidden":53},[66],[28,2154,2156,2159],{"className":2155},[70],[28,2157],{"className":2158,"style":154},[74],[28,2160,49],{"className":2161,"style":81},[79,80]," 的理想), ",[28,2164,2166,2189],{"className":2165},[31],[28,2167,2169],{"className":2168},[35],[37,2170,2171],{"xmlns":39},[41,2172,2173,2186],{},[44,2174,2175,2177,2179,2181,2184],{},[47,2176,1864],{"mathvariant":191},[51,2178,1363],{},[47,2180,110],{},[51,2182,2183],{},"≤",[47,2185,57],{},[59,2187,2188],{"encoding":61},"\\operatorname{Im} \\phi \\le S",[28,2190,2192,2219],{"className":2191,"ariaHidden":53},[66],[28,2193,2195,2198,2204,2207,2210,2213,2216],{"className":2194},[70],[28,2196],{"className":2197,"style":133},[74],[28,2199,2201],{"className":2200},[1385],[28,2202,1864],{"className":2203},[79,1389],[28,2205],{"className":2206,"style":90},[89],[28,2208,110],{"className":2209},[79,80],[28,2211],{"className":2212,"style":140},[89],[28,2214,2183],{"className":2215},[144],[28,2217],{"className":2218,"style":140},[89],[28,2220,2222,2225],{"className":2221},[70],[28,2223],{"className":2224,"style":154},[74],[28,2226,57],{"className":2227,"style":94},[79,80]," (像是 ",[28,2230,2232,2245],{"className":2231},[31],[28,2233,2235],{"className":2234},[35],[37,2236,2237],{"xmlns":39},[41,2238,2239,2243],{},[44,2240,2241],{},[47,2242,57],{},[59,2244,57],{"encoding":61},[28,2246,2248],{"className":2247,"ariaHidden":53},[66],[28,2249,2251,2254],{"className":2250},[70],[28,2252],{"className":2253,"style":154},[74],[28,2255,57],{"className":2256,"style":94},[79,80]," 的子环).\n(ii) ",[28,2259,2261,2274],{"className":2260},[31],[28,2262,2264],{"className":2263},[35],[37,2265,2266],{"xmlns":39},[41,2267,2268,2272],{},[44,2269,2270],{},[47,2271,110],{},[59,2273,520],{"encoding":61},[28,2275,2277],{"className":2276,"ariaHidden":53},[66],[28,2278,2280,2283],{"className":2279},[70],[28,2281],{"className":2282,"style":133},[74],[28,2284,110],{"className":2285},[79,80]," 是单射，当且仅当 ",[28,2288,2290,2316],{"className":2289},[31],[28,2291,2293],{"className":2292},[35],[37,2294,2295],{"xmlns":39},[41,2296,2297,2313],{},[44,2298,2299,2301,2303,2305,2307,2309,2311],{},[47,2300,1701],{},[51,2302,1363],{},[47,2304,110],{},[51,2306,282],{},[51,2308,1710],{"stretchy":268},[1731,2310,1733],{},[51,2312,1736],{"stretchy":268},[59,2314,2315],{"encoding":61},"\\ker \\phi = \\{0\\}",[28,2317,2319,2343],{"className":2318,"ariaHidden":53},[66],[28,2320,2322,2325,2328,2331,2334,2337,2340],{"className":2321},[70],[28,2323],{"className":2324,"style":133},[74],[28,2326,1701],{"className":2327},[1385],[28,2329],{"className":2330,"style":90},[89],[28,2332,110],{"className":2333},[79,80],[28,2335],{"className":2336,"style":140},[89],[28,2338,282],{"className":2339},[144],[28,2341],{"className":2342,"style":140},[89],[28,2344,2346,2349,2352,2355],{"className":2345},[70],[28,2347],{"className":2348,"style":349},[74],[28,2350,1710],{"className":2351},[356],[28,2353,1733],{"className":2354},[79],[28,2356,1736],{"className":2357},[383],[20,2359,2360],{},[23,2361,2362],{},"证明 (补全作业):",[20,2364,2365],{},[23,2366,2367,2368,2428,2429],{},"(i) 证明 ",[28,2369,2371,2392],{"className":2370},[31],[28,2372,2374],{"className":2373},[35],[37,2375,2376],{"xmlns":39},[41,2377,2378,2390],{},[44,2379,2380,2382,2384,2386,2388],{},[47,2381,1701],{},[51,2383,1363],{},[47,2385,110],{},[51,2387,2090],{},[47,2389,49],{},[59,2391,2095],{"encoding":61},[28,2393,2395,2419],{"className":2394,"ariaHidden":53},[66],[28,2396,2398,2401,2404,2407,2410,2413,2416],{"className":2397},[70],[28,2399],{"className":2400,"style":133},[74],[28,2402,1701],{"className":2403},[1385],[28,2405],{"className":2406,"style":90},[89],[28,2408,110],{"className":2409},[79,80],[28,2411],{"className":2412,"style":363},[89],[28,2414,2090],{"className":2415},[367,2120],[28,2417],{"className":2418,"style":363},[89],[28,2420,2422,2425],{"className":2421},[70],[28,2423],{"className":2424,"style":154},[74],[28,2426,49],{"className":2427,"style":81},[79,80]," 和 ",[28,2430,2432,2453],{"className":2431},[31],[28,2433,2435],{"className":2434},[35],[37,2436,2437],{"xmlns":39},[41,2438,2439,2451],{},[44,2440,2441,2443,2445,2447,2449],{},[47,2442,1864],{"mathvariant":191},[51,2444,1363],{},[47,2446,110],{},[51,2448,2183],{},[47,2450,57],{},[59,2452,2188],{"encoding":61},[28,2454,2456,2483],{"className":2455,"ariaHidden":53},[66],[28,2457,2459,2462,2468,2471,2474,2477,2480],{"className":2458},[70],[28,2460],{"className":2461,"style":133},[74],[28,2463,2465],{"className":2464},[1385],[28,2466,1864],{"className":2467},[79,1389],[28,2469],{"className":2470,"style":90},[89],[28,2472,110],{"className":2473},[79,80],[28,2475],{"className":2476,"style":140},[89],[28,2478,2183],{"className":2479},[144],[28,2481],{"className":2482,"style":140},[89],[28,2484,2486,2489],{"className":2485},[70],[28,2487],{"className":2488,"style":154},[74],[28,2490,57],{"className":2491,"style":94},[79,80],[1679,2493,2494,4331],{},[545,2495,2496,2567],{},[23,2497,2498,2499,1432,2538,2566],{},"1. 证明 ",[28,2500,2502,2520],{"className":2501},[31],[28,2503,2505],{"className":2504},[35],[37,2506,2507],{"xmlns":39},[41,2508,2509,2517],{},[44,2510,2511,2513,2515],{},[47,2512,1701],{},[51,2514,1363],{},[47,2516,110],{},[59,2518,2519],{"encoding":61},"\\ker \\phi",[28,2521,2523],{"className":2522,"ariaHidden":53},[66],[28,2524,2526,2529,2532,2535],{"className":2525},[70],[28,2527],{"className":2528,"style":133},[74],[28,2530,1701],{"className":2531},[1385],[28,2533],{"className":2534,"style":90},[89],[28,2536,110],{"className":2537},[79,80],[28,2539,2541,2554],{"className":2540},[31],[28,2542,2544],{"className":2543},[35],[37,2545,2546],{"xmlns":39},[41,2547,2548,2552],{},[44,2549,2550],{},[47,2551,49],{},[59,2553,49],{"encoding":61},[28,2555,2557],{"className":2556,"ariaHidden":53},[66],[28,2558,2560,2563],{"className":2559},[70],[28,2561],{"className":2562,"style":154},[74],[28,2564,49],{"className":2565,"style":81},[79,80]," 的理想:",[1679,2568,2569,2978,3485],{},[545,2570,2571,2574,2575,2603,2604,2770,2771,2873,2874,537],{},[23,2572,2573],{},"非空性",": 因为 ",[28,2576,2578,2591],{"className":2577},[31],[28,2579,2581],{"className":2580},[35],[37,2582,2583],{"xmlns":39},[41,2584,2585,2589],{},[44,2586,2587],{},[47,2588,110],{},[59,2590,520],{"encoding":61},[28,2592,2594],{"className":2593,"ariaHidden":53},[66],[28,2595,2597,2600],{"className":2596},[70],[28,2598],{"className":2599,"style":133},[74],[28,2601,110],{"className":2602},[79,80]," 是加法群同态，故 ",[28,2605,2607,2640],{"className":2606},[31],[28,2608,2610],{"className":2609},[35],[37,2611,2612],{"xmlns":39},[41,2613,2614,2637],{},[44,2615,2616,2618,2620,2627,2629,2631],{},[47,2617,110],{},[51,2619,269],{"stretchy":268},[2621,2622,2623,2625],"msub",{},[1731,2624,1733],{},[47,2626,49],{},[51,2628,279],{"stretchy":268},[51,2630,282],{},[2621,2632,2633,2635],{},[1731,2634,1733],{},[47,2636,57],{},[59,2638,2639],{"encoding":61},"\\phi(0_R) = 0_S",[28,2641,2643,2723],{"className":2642,"ariaHidden":53},[66],[28,2644,2646,2649,2652,2655,2711,2714,2717,2720],{"className":2645},[70],[28,2647],{"className":2648,"style":349},[74],[28,2650,110],{"className":2651},[79,80],[28,2653,269],{"className":2654},[356],[28,2656,2658,2661],{"className":2657},[79],[28,2659,1733],{"className":2660},[79],[28,2662,2665],{"className":2663},[2664],"msupsub",[28,2666,2670,2702],{"className":2667},[2668,2669],"vlist-t","vlist-t2",[28,2671,2674,2697],{"className":2672},[2673],"vlist-r",[28,2675,2679],{"className":2676,"style":2678},[2677],"vlist","height:0.3283em;",[28,2680,2682,2687],{"style":2681},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[28,2683],{"className":2684,"style":2686},[2685],"pstrut","height:2.7em;",[28,2688,2694],{"className":2689},[2690,2691,2692,2693],"sizing","reset-size6","size3","mtight",[28,2695,49],{"className":2696,"style":81},[79,80,2693],[28,2698,2701],{"className":2699},[2700],"vlist-s","​",[28,2703,2705],{"className":2704},[2673],[28,2706,2709],{"className":2707,"style":2708},[2677],"height:0.15em;",[28,2710],{},[28,2712,279],{"className":2713},[383],[28,2715],{"className":2716,"style":140},[89],[28,2718,282],{"className":2719},[144],[28,2721],{"className":2722,"style":140},[89],[28,2724,2726,2730],{"className":2725},[70],[28,2727],{"className":2728,"style":2729},[74],"height:0.7944em;vertical-align:-0.15em;",[28,2731,2733,2736],{"className":2732},[79],[28,2734,1733],{"className":2735},[79],[28,2737,2739],{"className":2738},[2664],[28,2740,2742,2762],{"className":2741},[2668,2669],[28,2743,2745,2759],{"className":2744},[2673],[28,2746,2748],{"className":2747,"style":2678},[2677],[28,2749,2750,2753],{"style":2681},[28,2751],{"className":2752,"style":2686},[2685],[28,2754,2756],{"className":2755},[2690,2691,2692,2693],[28,2757,57],{"className":2758,"style":94},[79,80,2693],[28,2760,2701],{"className":2761},[2700],[28,2763,2765],{"className":2764},[2673],[28,2766,2768],{"className":2767,"style":2708},[2677],[28,2769],{},"，所以 ",[28,2772,2774,2800],{"className":2773},[31],[28,2775,2777],{"className":2776},[35],[37,2778,2779],{"xmlns":39},[41,2780,2781,2797],{},[44,2782,2783,2789,2791,2793,2795],{},[2621,2784,2785,2787],{},[1731,2786,1733],{},[47,2788,49],{},[51,2790,203],{},[47,2792,1701],{},[51,2794,1363],{},[47,2796,110],{},[59,2798,2799],{"encoding":61},"0_R \\in \\ker \\phi",[28,2801,2803,2858],{"className":2802,"ariaHidden":53},[66],[28,2804,2806,2809,2849,2852,2855],{"className":2805},[70],[28,2807],{"className":2808,"style":2729},[74],[28,2810,2812,2815],{"className":2811},[79],[28,2813,1733],{"className":2814},[79],[28,2816,2818],{"className":2817},[2664],[28,2819,2821,2841],{"className":2820},[2668,2669],[28,2822,2824,2838],{"className":2823},[2673],[28,2825,2827],{"className":2826,"style":2678},[2677],[28,2828,2829,2832],{"style":2681},[28,2830],{"className":2831,"style":2686},[2685],[28,2833,2835],{"className":2834},[2690,2691,2692,2693],[28,2836,49],{"className":2837,"style":81},[79,80,2693],[28,2839,2701],{"className":2840},[2700],[28,2842,2844],{"className":2843},[2673],[28,2845,2847],{"className":2846,"style":2708},[2677],[28,2848],{},[28,2850],{"className":2851,"style":140},[89],[28,2853,203],{"className":2854},[144],[28,2856],{"className":2857,"style":140},[89],[28,2859,2861,2864,2867,2870],{"className":2860},[70],[28,2862],{"className":2863,"style":133},[74],[28,2865,1701],{"className":2866},[1385],[28,2868],{"className":2869,"style":90},[89],[28,2871,110],{"className":2872},[79,80],"，即 ",[28,2875,2877,2901],{"className":2876},[31],[28,2878,2880],{"className":2879},[35],[37,2881,2882],{"xmlns":39},[41,2883,2884,2898],{},[44,2885,2886,2888,2890,2892,2895],{},[47,2887,1701],{},[51,2889,1363],{},[47,2891,110],{},[51,2893,2894],{"mathvariant":191},"≠",[47,2896,2897],{"mathvariant":191},"∅",[59,2899,2900],{"encoding":61},"\\ker \\phi \\neq \\emptyset",[28,2902,2904,2968],{"className":2903,"ariaHidden":53},[66],[28,2905,2907,2910,2913,2916,2919,2922,2965],{"className":2906},[70],[28,2908],{"className":2909,"style":133},[74],[28,2911,1701],{"className":2912},[1385],[28,2914],{"className":2915,"style":90},[89],[28,2917,110],{"className":2918},[79,80],[28,2920],{"className":2921,"style":140},[89],[28,2923,2925,2958,2962],{"className":2924},[144],[28,2926,2928],{"className":2927},[144],[28,2929,2932],{"className":2930},[79,2931],"vbox",[28,2933,2936],{"className":2934},[2935],"thinbox",[28,2937,2940,2943,2954],{"className":2938},[2939],"rlap",[28,2941],{"className":2942,"style":133},[74],[28,2944,2947],{"className":2945},[2946],"inner",[28,2948,2950],{"className":2949},[79],[28,2951,2953],{"className":2952},[144],"",[28,2955],{"className":2956},[2957],"fix",[28,2959],{"className":2960},[89,2961],"nobreak",[28,2963,282],{"className":2964},[144],[28,2966],{"className":2967,"style":140},[89],[28,2969,2971,2975],{"className":2970},[70],[28,2972],{"className":2973,"style":2974},[74],"height:0.8056em;vertical-align:-0.0556em;",[28,2976,2897],{"className":2977},[79],[545,2979,2980,1686,2983,3062,3063,3180,3181],{},[23,2981,2982],{},"加法封闭性 (对减法封闭)",[28,2984,2986,3014],{"className":2985},[31],[28,2987,2989],{"className":2988},[35],[37,2990,2991],{"xmlns":39},[41,2992,2993,3011],{},[44,2994,2995,2997,2999,3001,3003,3005,3007,3009],{},[47,2996,192],{"mathvariant":191},[47,2998,195],{},[51,3000,54],{"separator":53},[47,3002,200],{},[51,3004,203],{},[47,3006,1701],{},[51,3008,1363],{},[47,3010,110],{},[59,3012,3013],{"encoding":61},"\\forall a, b \\in \\ker \\phi",[28,3015,3017,3047],{"className":3016,"ariaHidden":53},[66],[28,3018,3020,3023,3026,3029,3032,3035,3038,3041,3044],{"className":3019},[70],[28,3021],{"className":3022,"style":133},[74],[28,3024,192],{"className":3025},[79],[28,3027,195],{"className":3028},[79,80],[28,3030,54],{"className":3031},[85],[28,3033],{"className":3034,"style":90},[89],[28,3036,200],{"className":3037},[79,80],[28,3039],{"className":3040,"style":140},[89],[28,3042,203],{"className":3043},[144],[28,3045],{"className":3046,"style":140},[89],[28,3048,3050,3053,3056,3059],{"className":3049},[70],[28,3051],{"className":3052,"style":133},[74],[28,3054,1701],{"className":3055},[1385],[28,3057],{"className":3058,"style":90},[89],[28,3060,110],{"className":3061},[79,80],"，有 ",[28,3064,3066,3104],{"className":3065},[31],[28,3067,3069],{"className":3068},[35],[37,3070,3071],{"xmlns":39},[41,3072,3073,3101],{},[44,3074,3075,3077,3079,3081,3083,3085,3087,3089,3091,3093,3095,3097,3099],{},[47,3076,110],{},[51,3078,269],{"stretchy":268},[47,3080,195],{},[51,3082,279],{"stretchy":268},[51,3084,282],{},[1731,3086,1733],{},[51,3088,54],{"separator":53},[47,3090,110],{},[51,3092,269],{"stretchy":268},[47,3094,200],{},[51,3096,279],{"stretchy":268},[51,3098,282],{},[1731,3100,1733],{},[59,3102,3103],{"encoding":61},"\\phi(a)=0, \\phi(b)=0",[28,3105,3107,3134,3170],{"className":3106,"ariaHidden":53},[66],[28,3108,3110,3113,3116,3119,3122,3125,3128,3131],{"className":3109},[70],[28,3111],{"className":3112,"style":349},[74],[28,3114,110],{"className":3115},[79,80],[28,3117,269],{"className":3118},[356],[28,3120,195],{"className":3121},[79,80],[28,3123,279],{"className":3124},[383],[28,3126],{"className":3127,"style":140},[89],[28,3129,282],{"className":3130},[144],[28,3132],{"className":3133,"style":140},[89],[28,3135,3137,3140,3143,3146,3149,3152,3155,3158,3161,3164,3167],{"className":3136},[70],[28,3138],{"className":3139,"style":349},[74],[28,3141,1733],{"className":3142},[79],[28,3144,54],{"className":3145},[85],[28,3147],{"className":3148,"style":90},[89],[28,3150,110],{"className":3151},[79,80],[28,3153,269],{"className":3154},[356],[28,3156,200],{"className":3157},[79,80],[28,3159,279],{"className":3160},[383],[28,3162],{"className":3163,"style":140},[89],[28,3165,282],{"className":3166},[144],[28,3168],{"className":3169,"style":140},[89],[28,3171,3173,3177],{"className":3172},[70],[28,3174],{"className":3175,"style":3176},[74],"height:0.6444em;",[28,3178,1733],{"className":3179},[79],"。\n",[28,3182,3184,3266],{"className":3183},[31],[28,3185,3187],{"className":3186},[35],[37,3188,3189],{"xmlns":39},[41,3190,3191,3263],{},[44,3192,3193,3195,3197,3199,3202,3204,3206,3208,3210,3212,3214,3216,3218,3220,3222,3224,3226,3228,3230,3232,3234,3236,3238,3242,3245,3247,3249,3251,3253,3255,3257,3259,3261],{},[47,3194,110],{},[51,3196,269],{"stretchy":268},[47,3198,195],{},[51,3200,3201],{},"−",[47,3203,200],{},[51,3205,279],{"stretchy":268},[51,3207,282],{},[47,3209,110],{},[51,3211,269],{"stretchy":268},[47,3213,195],{},[51,3215,279],{"stretchy":268},[51,3217,3201],{},[47,3219,110],{},[51,3221,269],{"stretchy":268},[47,3223,200],{},[51,3225,279],{"stretchy":268},[51,3227,282],{},[1731,3229,1733],{},[51,3231,3201],{},[1731,3233,1733],{},[51,3235,282],{},[1731,3237,1733],{},[3239,3240,3241],"mtext",{},"  ",[51,3243,3244],{},"⟹",[3239,3246,3241],{},[47,3248,195],{},[51,3250,3201],{},[47,3252,200],{},[51,3254,203],{},[47,3256,1701],{},[51,3258,1363],{},[47,3260,110],{},[47,3262,336],{"mathvariant":191},[59,3264,3265],{"encoding":61},"\\phi(a-b) = \\phi(a) - \\phi(b) = 0 - 0 = 0 \\implies a-b \\in \\ker \\phi.",[28,3267,3269,3293,3314,3341,3368,3387,3405,3430,3449,3467],{"className":3268,"ariaHidden":53},[66],[28,3270,3272,3275,3278,3281,3284,3287,3290],{"className":3271},[70],[28,3273],{"className":3274,"style":349},[74],[28,3276,110],{"className":3277},[79,80],[28,3279,269],{"className":3280},[356],[28,3282,195],{"className":3283},[79,80],[28,3285],{"className":3286,"style":363},[89],[28,3288,3201],{"className":3289},[367],[28,3291],{"className":3292,"style":363},[89],[28,3294,3296,3299,3302,3305,3308,3311],{"className":3295},[70],[28,3297],{"className":3298,"style":349},[74],[28,3300,200],{"className":3301},[79,80],[28,3303,279],{"className":3304},[383],[28,3306],{"className":3307,"style":140},[89],[28,3309,282],{"className":3310},[144],[28,3312],{"className":3313,"style":140},[89],[28,3315,3317,3320,3323,3326,3329,3332,3335,3338],{"className":3316},[70],[28,3318],{"className":3319,"style":349},[74],[28,3321,110],{"className":3322},[79,80],[28,3324,269],{"className":3325},[356],[28,3327,195],{"className":3328},[79,80],[28,3330,279],{"className":3331},[383],[28,3333],{"className":3334,"style":363},[89],[28,3336,3201],{"className":3337},[367],[28,3339],{"className":3340,"style":363},[89],[28,3342,3344,3347,3350,3353,3356,3359,3362,3365],{"className":3343},[70],[28,3345],{"className":3346,"style":349},[74],[28,3348,110],{"className":3349},[79,80],[28,3351,269],{"className":3352},[356],[28,3354,200],{"className":3355},[79,80],[28,3357,279],{"className":3358},[383],[28,3360],{"className":3361,"style":140},[89],[28,3363,282],{"className":3364},[144],[28,3366],{"className":3367,"style":140},[89],[28,3369,3371,3375,3378,3381,3384],{"className":3370},[70],[28,3372],{"className":3373,"style":3374},[74],"height:0.7278em;vertical-align:-0.0833em;",[28,3376,1733],{"className":3377},[79],[28,3379],{"className":3380,"style":363},[89],[28,3382,3201],{"className":3383},[367],[28,3385],{"className":3386,"style":363},[89],[28,3388,3390,3393,3396,3399,3402],{"className":3389},[70],[28,3391],{"className":3392,"style":3176},[74],[28,3394,1733],{"className":3395},[79],[28,3397],{"className":3398,"style":140},[89],[28,3400,282],{"className":3401},[144],[28,3403],{"className":3404,"style":140},[89],[28,3406,3408,3412,3415,3418,3421,3424,3427],{"className":3407},[70],[28,3409],{"className":3410,"style":3411},[74],"height:0.6684em;vertical-align:-0.024em;",[28,3413,1733],{"className":3414},[79],[28,3416],{"className":3417,"style":140},[89],[28,3419],{"className":3420,"style":140},[89],[28,3422,3244],{"className":3423},[144],[28,3425],{"className":3426,"style":140},[89],[28,3428],{"className":3429,"style":140},[89],[28,3431,3433,3437,3440,3443,3446],{"className":3432},[70],[28,3434],{"className":3435,"style":3436},[74],"height:0.6667em;vertical-align:-0.0833em;",[28,3438,195],{"className":3439},[79,80],[28,3441],{"className":3442,"style":363},[89],[28,3444,3201],{"className":3445},[367],[28,3447],{"className":3448,"style":363},[89],[28,3450,3452,3455,3458,3461,3464],{"className":3451},[70],[28,3453],{"className":3454,"style":893},[74],[28,3456,200],{"className":3457},[79,80],[28,3459],{"className":3460,"style":140},[89],[28,3462,203],{"className":3463},[144],[28,3465],{"className":3466,"style":140},[89],[28,3468,3470,3473,3476,3479,3482],{"className":3469},[70],[28,3471],{"className":3472,"style":133},[74],[28,3474,1701],{"className":3475},[1385],[28,3477],{"className":3478,"style":90},[89],[28,3480,110],{"className":3481},[79,80],[28,3483,336],{"className":3484},[79],[545,3486,3487,1686,3490,3556,3557,3623,3624,3180,3680,3942,4203,4204,1432,4242,4270,4271,537],{},[23,3488,3489],{},"吸收律",[28,3491,3493,3517],{"className":3492},[31],[28,3494,3496],{"className":3495},[35],[37,3497,3498],{"xmlns":39},[41,3499,3500,3514],{},[44,3501,3502,3504,3506,3508,3510,3512],{},[47,3503,192],{"mathvariant":191},[47,3505,195],{},[51,3507,203],{},[47,3509,1701],{},[51,3511,1363],{},[47,3513,110],{},[59,3515,3516],{"encoding":61},"\\forall a \\in \\ker \\phi",[28,3518,3520,3541],{"className":3519,"ariaHidden":53},[66],[28,3521,3523,3526,3529,3532,3535,3538],{"className":3522},[70],[28,3524],{"className":3525,"style":893},[74],[28,3527,192],{"className":3528},[79],[28,3530,195],{"className":3531},[79,80],[28,3533],{"className":3534,"style":140},[89],[28,3536,203],{"className":3537},[144],[28,3539],{"className":3540,"style":140},[89],[28,3542,3544,3547,3550,3553],{"className":3543},[70],[28,3545],{"className":3546,"style":133},[74],[28,3548,1701],{"className":3549},[1385],[28,3551],{"className":3552,"style":90},[89],[28,3554,110],{"className":3555},[79,80]," (即 ",[28,3558,3560,3584],{"className":3559},[31],[28,3561,3563],{"className":3562},[35],[37,3564,3565],{"xmlns":39},[41,3566,3567,3581],{},[44,3568,3569,3571,3573,3575,3577,3579],{},[47,3570,110],{},[51,3572,269],{"stretchy":268},[47,3574,195],{},[51,3576,279],{"stretchy":268},[51,3578,282],{},[1731,3580,1733],{},[59,3582,3583],{"encoding":61},"\\phi(a)=0",[28,3585,3587,3614],{"className":3586,"ariaHidden":53},[66],[28,3588,3590,3593,3596,3599,3602,3605,3608,3611],{"className":3589},[70],[28,3591],{"className":3592,"style":349},[74],[28,3594,110],{"className":3595},[79,80],[28,3597,269],{"className":3598},[356],[28,3600,195],{"className":3601},[79,80],[28,3603,279],{"className":3604},[383],[28,3606],{"className":3607,"style":140},[89],[28,3609,282],{"className":3610},[144],[28,3612],{"className":3613,"style":140},[89],[28,3615,3617,3620],{"className":3616},[70],[28,3618],{"className":3619,"style":3176},[74],[28,3621,1733],{"className":3622},[79],"), ",[28,3625,3627,3647],{"className":3626},[31],[28,3628,3630],{"className":3629},[35],[37,3631,3632],{"xmlns":39},[41,3633,3634,3644],{},[44,3635,3636,3638,3640,3642],{},[47,3637,192],{"mathvariant":191},[47,3639,876],{},[51,3641,203],{},[47,3643,49],{},[59,3645,3646],{"encoding":61},"\\forall r \\in R",[28,3648,3650,3671],{"className":3649,"ariaHidden":53},[66],[28,3651,3653,3656,3659,3662,3665,3668],{"className":3652},[70],[28,3654],{"className":3655,"style":893},[74],[28,3657,192],{"className":3658},[79],[28,3660,876],{"className":3661,"style":930},[79,80],[28,3663],{"className":3664,"style":140},[89],[28,3666,203],{"className":3667},[144],[28,3669],{"className":3670,"style":140},[89],[28,3672,3674,3677],{"className":3673},[70],[28,3675],{"className":3676,"style":154},[74],[28,3678,49],{"className":3679,"style":81},[79,80],[28,3681,3683,3762],{"className":3682},[31],[28,3684,3686],{"className":3685},[35],[37,3687,3688],{"xmlns":39},[41,3689,3690,3759],{},[44,3691,3692,3694,3696,3698,3700,3702,3704,3706,3708,3710,3712,3714,3716,3718,3720,3722,3724,3726,3728,3730,3733,3735,3737,3739,3741,3743,3745,3747,3749,3751,3753,3755,3757],{},[47,3693,110],{},[51,3695,269],{"stretchy":268},[47,3697,876],{},[47,3699,195],{},[51,3701,279],{"stretchy":268},[51,3703,282],{},[47,3705,110],{},[51,3707,269],{"stretchy":268},[47,3709,876],{},[51,3711,279],{"stretchy":268},[47,3713,110],{},[51,3715,269],{"stretchy":268},[47,3717,195],{},[51,3719,279],{"stretchy":268},[51,3721,282],{},[47,3723,110],{},[51,3725,269],{"stretchy":268},[47,3727,876],{},[51,3729,279],{"stretchy":268},[51,3731,3732],{},"⋅",[1731,3734,1733],{},[51,3736,282],{},[1731,3738,1733],{},[3239,3740,3241],{},[51,3742,3244],{},[3239,3744,3241],{},[47,3746,876],{},[47,3748,195],{},[51,3750,203],{},[47,3752,1701],{},[51,3754,1363],{},[47,3756,110],{},[47,3758,336],{"mathvariant":191},[59,3760,3761],{"encoding":61},"\\phi(ra) = \\phi(r)\\phi(a) = \\phi(r) \\cdot 0 = 0 \\implies ra \\in \\ker \\phi.",[28,3763,3765,3795,3834,3861,3879,3903,3924],{"className":3764,"ariaHidden":53},[66],[28,3766,3768,3771,3774,3777,3780,3783,3786,3789,3792],{"className":3767},[70],[28,3769],{"className":3770,"style":349},[74],[28,3772,110],{"className":3773},[79,80],[28,3775,269],{"className":3776},[356],[28,3778,876],{"className":3779,"style":930},[79,80],[28,3781,195],{"className":3782},[79,80],[28,3784,279],{"className":3785},[383],[28,3787],{"className":3788,"style":140},[89],[28,3790,282],{"className":3791},[144],[28,3793],{"className":3794,"style":140},[89],[28,3796,3798,3801,3804,3807,3810,3813,3816,3819,3822,3825,3828,3831],{"className":3797},[70],[28,3799],{"className":3800,"style":349},[74],[28,3802,110],{"className":3803},[79,80],[28,3805,269],{"className":3806},[356],[28,3808,876],{"className":3809,"style":930},[79,80],[28,3811,279],{"className":3812},[383],[28,3814,110],{"className":3815},[79,80],[28,3817,269],{"className":3818},[356],[28,3820,195],{"className":3821},[79,80],[28,3823,279],{"className":3824},[383],[28,3826],{"className":3827,"style":140},[89],[28,3829,282],{"className":3830},[144],[28,3832],{"className":3833,"style":140},[89],[28,3835,3837,3840,3843,3846,3849,3852,3855,3858],{"className":3836},[70],[28,3838],{"className":3839,"style":349},[74],[28,3841,110],{"className":3842},[79,80],[28,3844,269],{"className":3845},[356],[28,3847,876],{"className":3848,"style":930},[79,80],[28,3850,279],{"className":3851},[383],[28,3853],{"className":3854,"style":363},[89],[28,3856,3732],{"className":3857},[367],[28,3859],{"className":3860,"style":363},[89],[28,3862,3864,3867,3870,3873,3876],{"className":3863},[70],[28,3865],{"className":3866,"style":3176},[74],[28,3868,1733],{"className":3869},[79],[28,3871],{"className":3872,"style":140},[89],[28,3874,282],{"className":3875},[144],[28,3877],{"className":3878,"style":140},[89],[28,3880,3882,3885,3888,3891,3894,3897,3900],{"className":3881},[70],[28,3883],{"className":3884,"style":3411},[74],[28,3886,1733],{"className":3887},[79],[28,3889],{"className":3890,"style":140},[89],[28,3892],{"className":3893,"style":140},[89],[28,3895,3244],{"className":3896},[144],[28,3898],{"className":3899,"style":140},[89],[28,3901],{"className":3902,"style":140},[89],[28,3904,3906,3909,3912,3915,3918,3921],{"className":3905},[70],[28,3907],{"className":3908,"style":1960},[74],[28,3910,876],{"className":3911,"style":930},[79,80],[28,3913,195],{"className":3914},[79,80],[28,3916],{"className":3917,"style":140},[89],[28,3919,203],{"className":3920},[144],[28,3922],{"className":3923,"style":140},[89],[28,3925,3927,3930,3933,3936,3939],{"className":3926},[70],[28,3928],{"className":3929,"style":133},[74],[28,3931,1701],{"className":3932},[1385],[28,3934],{"className":3935,"style":90},[89],[28,3937,110],{"className":3938},[79,80],[28,3940,336],{"className":3941},[79],[28,3943,3945,4023],{"className":3944},[31],[28,3946,3948],{"className":3947},[35],[37,3949,3950],{"xmlns":39},[41,3951,3952,4020],{},[44,3953,3954,3956,3958,3960,3962,3964,3966,3968,3970,3972,3974,3976,3978,3980,3982,3984,3986,3988,3990,3992,3994,3996,3998,4000,4002,4004,4006,4008,4010,4012,4014,4016,4018],{},[47,3955,110],{},[51,3957,269],{"stretchy":268},[47,3959,195],{},[47,3961,876],{},[51,3963,279],{"stretchy":268},[51,3965,282],{},[47,3967,110],{},[51,3969,269],{"stretchy":268},[47,3971,195],{},[51,3973,279],{"stretchy":268},[47,3975,110],{},[51,3977,269],{"stretchy":268},[47,3979,876],{},[51,3981,279],{"stretchy":268},[51,3983,282],{},[1731,3985,1733],{},[51,3987,3732],{},[47,3989,110],{},[51,3991,269],{"stretchy":268},[47,3993,876],{},[51,3995,279],{"stretchy":268},[51,3997,282],{},[1731,3999,1733],{},[3239,4001,3241],{},[51,4003,3244],{},[3239,4005,3241],{},[47,4007,195],{},[47,4009,876],{},[51,4011,203],{},[47,4013,1701],{},[51,4015,1363],{},[47,4017,110],{},[47,4019,336],{"mathvariant":191},[59,4021,4022],{"encoding":61},"\\phi(ar) = \\phi(a)\\phi(r) = 0 \\cdot \\phi(r) = 0 \\implies ar \\in \\ker \\phi.",[28,4024,4026,4056,4095,4113,4140,4164,4185],{"className":4025,"ariaHidden":53},[66],[28,4027,4029,4032,4035,4038,4041,4044,4047,4050,4053],{"className":4028},[70],[28,4030],{"className":4031,"style":349},[74],[28,4033,110],{"className":4034},[79,80],[28,4036,269],{"className":4037},[356],[28,4039,195],{"className":4040},[79,80],[28,4042,876],{"className":4043,"style":930},[79,80],[28,4045,279],{"className":4046},[383],[28,4048],{"className":4049,"style":140},[89],[28,4051,282],{"className":4052},[144],[28,4054],{"className":4055,"style":140},[89],[28,4057,4059,4062,4065,4068,4071,4074,4077,4080,4083,4086,4089,4092],{"className":4058},[70],[28,4060],{"className":4061,"style":349},[74],[28,4063,110],{"className":4064},[79,80],[28,4066,269],{"className":4067},[356],[28,4069,195],{"className":4070},[79,80],[28,4072,279],{"className":4073},[383],[28,4075,110],{"className":4076},[79,80],[28,4078,269],{"className":4079},[356],[28,4081,876],{"className":4082,"style":930},[79,80],[28,4084,279],{"className":4085},[383],[28,4087],{"className":4088,"style":140},[89],[28,4090,282],{"className":4091},[144],[28,4093],{"className":4094,"style":140},[89],[28,4096,4098,4101,4104,4107,4110],{"className":4097},[70],[28,4099],{"className":4100,"style":3176},[74],[28,4102,1733],{"className":4103},[79],[28,4105],{"className":4106,"style":363},[89],[28,4108,3732],{"className":4109},[367],[28,4111],{"className":4112,"style":363},[89],[28,4114,4116,4119,4122,4125,4128,4131,4134,4137],{"className":4115},[70],[28,4117],{"className":4118,"style":349},[74],[28,4120,110],{"className":4121},[79,80],[28,4123,269],{"className":4124},[356],[28,4126,876],{"className":4127,"style":930},[79,80],[28,4129,279],{"className":4130},[383],[28,4132],{"className":4133,"style":140},[89],[28,4135,282],{"className":4136},[144],[28,4138],{"className":4139,"style":140},[89],[28,4141,4143,4146,4149,4152,4155,4158,4161],{"className":4142},[70],[28,4144],{"className":4145,"style":3411},[74],[28,4147,1733],{"className":4148},[79],[28,4150],{"className":4151,"style":140},[89],[28,4153],{"className":4154,"style":140},[89],[28,4156,3244],{"className":4157},[144],[28,4159],{"className":4160,"style":140},[89],[28,4162],{"className":4163,"style":140},[89],[28,4165,4167,4170,4173,4176,4179,4182],{"className":4166},[70],[28,4168],{"className":4169,"style":1960},[74],[28,4171,195],{"className":4172},[79,80],[28,4174,876],{"className":4175,"style":930},[79,80],[28,4177],{"className":4178,"style":140},[89],[28,4180,203],{"className":4181},[144],[28,4183],{"className":4184,"style":140},[89],[28,4186,4188,4191,4194,4197,4200],{"className":4187},[70],[28,4189],{"className":4190,"style":133},[74],[28,4192,1701],{"className":4193},[1385],[28,4195],{"className":4196,"style":90},[89],[28,4198,110],{"className":4199},[79,80],[28,4201,336],{"className":4202},[79],"\n综上，",[28,4205,4207,4224],{"className":4206},[31],[28,4208,4210],{"className":4209},[35],[37,4211,4212],{"xmlns":39},[41,4213,4214,4222],{},[44,4215,4216,4218,4220],{},[47,4217,1701],{},[51,4219,1363],{},[47,4221,110],{},[59,4223,2519],{"encoding":61},[28,4225,4227],{"className":4226,"ariaHidden":53},[66],[28,4228,4230,4233,4236,4239],{"className":4229},[70],[28,4231],{"className":4232,"style":133},[74],[28,4234,1701],{"className":4235},[1385],[28,4237],{"className":4238,"style":90},[89],[28,4240,110],{"className":4241},[79,80],[28,4243,4245,4258],{"className":4244},[31],[28,4246,4248],{"className":4247},[35],[37,4249,4250],{"xmlns":39},[41,4251,4252,4256],{},[44,4253,4254],{},[47,4255,49],{},[59,4257,49],{"encoding":61},[28,4259,4261],{"className":4260,"ariaHidden":53},[66],[28,4262,4264,4267],{"className":4263},[70],[28,4265],{"className":4266,"style":154},[74],[28,4268,49],{"className":4269,"style":81},[79,80]," 的理想，即 ",[28,4272,4274,4295],{"className":4273},[31],[28,4275,4277],{"className":4276},[35],[37,4278,4279],{"xmlns":39},[41,4280,4281,4293],{},[44,4282,4283,4285,4287,4289,4291],{},[47,4284,1701],{},[51,4286,1363],{},[47,4288,110],{},[51,4290,2090],{},[47,4292,49],{},[59,4294,2095],{"encoding":61},[28,4296,4298,4322],{"className":4297,"ariaHidden":53},[66],[28,4299,4301,4304,4307,4310,4313,4316,4319],{"className":4300},[70],[28,4302],{"className":4303,"style":133},[74],[28,4305,1701],{"className":4306},[1385],[28,4308],{"className":4309,"style":90},[89],[28,4311,110],{"className":4312},[79,80],[28,4314],{"className":4315,"style":363},[89],[28,4317,2090],{"className":4318},[367,2120],[28,4320],{"className":4321,"style":363},[89],[28,4323,4325,4328],{"className":4324},[70],[28,4326],{"className":4327,"style":154},[74],[28,4329,49],{"className":4330,"style":81},[79,80],[545,4332,4333,4407],{},[23,4334,4335,4336,1432,4378,4406],{},"2. 证明 ",[28,4337,4339,4357],{"className":4338},[31],[28,4340,4342],{"className":4341},[35],[37,4343,4344],{"xmlns":39},[41,4345,4346,4354],{},[44,4347,4348,4350,4352],{},[47,4349,1864],{"mathvariant":191},[51,4351,1363],{},[47,4353,110],{},[59,4355,4356],{"encoding":61},"\\operatorname{Im} \\phi",[28,4358,4360],{"className":4359,"ariaHidden":53},[66],[28,4361,4363,4366,4372,4375],{"className":4362},[70],[28,4364],{"className":4365,"style":133},[74],[28,4367,4369],{"className":4368},[1385],[28,4370,1864],{"className":4371},[79,1389],[28,4373],{"className":4374,"style":90},[89],[28,4376,110],{"className":4377},[79,80],[28,4379,4381,4394],{"className":4380},[31],[28,4382,4384],{"className":4383},[35],[37,4385,4386],{"xmlns":39},[41,4387,4388,4392],{},[44,4389,4390],{},[47,4391,57],{},[59,4393,57],{"encoding":61},[28,4395,4397],{"className":4396,"ariaHidden":53},[66],[28,4398,4400,4403],{"className":4399},[70],[28,4401],{"className":4402,"style":154},[74],[28,4404,57],{"className":4405,"style":94},[79,80]," 的子环:",[1679,4408,4409,4905],{},[545,4410,4411,1686,4414,4499,4500,949,4564,3180,4680],{},[23,4412,4413],{},"减法封闭",[28,4415,4417,4447],{"className":4416},[31],[28,4418,4420],{"className":4419},[35],[37,4421,4422],{"xmlns":39},[41,4423,4424,4444],{},[44,4425,4426,4428,4431,4433,4436,4438,4440,4442],{},[47,4427,192],{"mathvariant":191},[47,4429,4430],{},"x",[51,4432,54],{"separator":53},[47,4434,4435],{},"y",[51,4437,203],{},[47,4439,1864],{"mathvariant":191},[51,4441,1363],{},[47,4443,110],{},[59,4445,4446],{"encoding":61},"\\forall x, y \\in \\operatorname{Im} \\phi",[28,4448,4450,4481],{"className":4449,"ariaHidden":53},[66],[28,4451,4453,4456,4459,4462,4465,4468,4472,4475,4478],{"className":4452},[70],[28,4454],{"className":4455,"style":133},[74],[28,4457,192],{"className":4458},[79],[28,4460,4430],{"className":4461},[79,80],[28,4463,54],{"className":4464},[85],[28,4466],{"className":4467,"style":90},[89],[28,4469,4435],{"className":4470,"style":4471},[79,80],"margin-right:0.0359em;",[28,4473],{"className":4474,"style":140},[89],[28,4476,203],{"className":4477},[144],[28,4479],{"className":4480,"style":140},[89],[28,4482,4484,4487,4493,4496],{"className":4483},[70],[28,4485],{"className":4486,"style":133},[74],[28,4488,4490],{"className":4489},[1385],[28,4491,1864],{"className":4492},[79,1389],[28,4494],{"className":4495,"style":90},[89],[28,4497,110],{"className":4498},[79,80],"，存在 ",[28,4501,4503,4525],{"className":4502},[31],[28,4504,4506],{"className":4505},[35],[37,4507,4508],{"xmlns":39},[41,4509,4510,4522],{},[44,4511,4512,4514,4516,4518,4520],{},[47,4513,195],{},[51,4515,54],{"separator":53},[47,4517,200],{},[51,4519,203],{},[47,4521,49],{},[59,4523,4524],{"encoding":61},"a, b \\in R",[28,4526,4528,4555],{"className":4527,"ariaHidden":53},[66],[28,4529,4531,4534,4537,4540,4543,4546,4549,4552],{"className":4530},[70],[28,4532],{"className":4533,"style":133},[74],[28,4535,195],{"className":4536},[79,80],[28,4538,54],{"className":4539},[85],[28,4541],{"className":4542,"style":90},[89],[28,4544,200],{"className":4545},[79,80],[28,4547],{"className":4548,"style":140},[89],[28,4550,203],{"className":4551},[144],[28,4553],{"className":4554,"style":140},[89],[28,4556,4558,4561],{"className":4557},[70],[28,4559],{"className":4560,"style":154},[74],[28,4562,49],{"className":4563,"style":81},[79,80],[28,4565,4567,4605],{"className":4566},[31],[28,4568,4570],{"className":4569},[35],[37,4571,4572],{"xmlns":39},[41,4573,4574,4602],{},[44,4575,4576,4578,4580,4582,4584,4586,4588,4590,4592,4594,4596,4598,4600],{},[47,4577,4430],{},[51,4579,282],{},[47,4581,110],{},[51,4583,269],{"stretchy":268},[47,4585,195],{},[51,4587,279],{"stretchy":268},[51,4589,54],{"separator":53},[47,4591,4435],{},[51,4593,282],{},[47,4595,110],{},[51,4597,269],{"stretchy":268},[47,4599,200],{},[51,4601,279],{"stretchy":268},[59,4603,4604],{"encoding":61},"x=\\phi(a), y=\\phi(b)",[28,4606,4608,4626,4662],{"className":4607,"ariaHidden":53},[66],[28,4609,4611,4614,4617,4620,4623],{"className":4610},[70],[28,4612],{"className":4613,"style":761},[74],[28,4615,4430],{"className":4616},[79,80],[28,4618],{"className":4619,"style":140},[89],[28,4621,282],{"className":4622},[144],[28,4624],{"className":4625,"style":140},[89],[28,4627,4629,4632,4635,4638,4641,4644,4647,4650,4653,4656,4659],{"className":4628},[70],[28,4630],{"className":4631,"style":349},[74],[28,4633,110],{"className":4634},[79,80],[28,4636,269],{"className":4637},[356],[28,4639,195],{"className":4640},[79,80],[28,4642,279],{"className":4643},[383],[28,4645,54],{"className":4646},[85],[28,4648],{"className":4649,"style":90},[89],[28,4651,4435],{"className":4652,"style":4471},[79,80],[28,4654],{"className":4655,"style":140},[89],[28,4657,282],{"className":4658},[144],[28,4660],{"className":4661,"style":140},[89],[28,4663,4665,4668,4671,4674,4677],{"className":4664},[70],[28,4666],{"className":4667,"style":349},[74],[28,4669,110],{"className":4670},[79,80],[28,4672,269],{"className":4673},[356],[28,4675,200],{"className":4676},[79,80],[28,4678,279],{"className":4679},[383],[28,4681,4683,4745],{"className":4682},[31],[28,4684,4686],{"className":4685},[35],[37,4687,4688],{"xmlns":39},[41,4689,4690,4742],{},[44,4691,4692,4694,4696,4698,4700,4702,4704,4706,4708,4710,4712,4714,4716,4718,4720,4722,4724,4726,4728,4730,4732,4734,4736,4738,4740],{},[47,4693,4430],{},[51,4695,3201],{},[47,4697,4435],{},[51,4699,282],{},[47,4701,110],{},[51,4703,269],{"stretchy":268},[47,4705,195],{},[51,4707,279],{"stretchy":268},[51,4709,3201],{},[47,4711,110],{},[51,4713,269],{"stretchy":268},[47,4715,200],{},[51,4717,279],{"stretchy":268},[51,4719,282],{},[47,4721,110],{},[51,4723,269],{"stretchy":268},[47,4725,195],{},[51,4727,3201],{},[47,4729,200],{},[51,4731,279],{"stretchy":268},[51,4733,203],{},[47,4735,1864],{"mathvariant":191},[51,4737,1363],{},[47,4739,110],{},[47,4741,336],{"mathvariant":191},[59,4743,4744],{"encoding":61},"x - y = \\phi(a) - \\phi(b) = \\phi(a-b) \\in \\operatorname{Im} \\phi.",[28,4746,4748,4766,4785,4812,4839,4863,4884],{"className":4747,"ariaHidden":53},[66],[28,4749,4751,4754,4757,4760,4763],{"className":4750},[70],[28,4752],{"className":4753,"style":3436},[74],[28,4755,4430],{"className":4756},[79,80],[28,4758],{"className":4759,"style":363},[89],[28,4761,3201],{"className":4762},[367],[28,4764],{"className":4765,"style":363},[89],[28,4767,4769,4773,4776,4779,4782],{"className":4768},[70],[28,4770],{"className":4771,"style":4772},[74],"height:0.625em;vertical-align:-0.1944em;",[28,4774,4435],{"className":4775,"style":4471},[79,80],[28,4777],{"className":4778,"style":140},[89],[28,4780,282],{"className":4781},[144],[28,4783],{"className":4784,"style":140},[89],[28,4786,4788,4791,4794,4797,4800,4803,4806,4809],{"className":4787},[70],[28,4789],{"className":4790,"style":349},[74],[28,4792,110],{"className":4793},[79,80],[28,4795,269],{"className":4796},[356],[28,4798,195],{"className":4799},[79,80],[28,4801,279],{"className":4802},[383],[28,4804],{"className":4805,"style":363},[89],[28,4807,3201],{"className":4808},[367],[28,4810],{"className":4811,"style":363},[89],[28,4813,4815,4818,4821,4824,4827,4830,4833,4836],{"className":4814},[70],[28,4816],{"className":4817,"style":349},[74],[28,4819,110],{"className":4820},[79,80],[28,4822,269],{"className":4823},[356],[28,4825,200],{"className":4826},[79,80],[28,4828,279],{"className":4829},[383],[28,4831],{"className":4832,"style":140},[89],[28,4834,282],{"className":4835},[144],[28,4837],{"className":4838,"style":140},[89],[28,4840,4842,4845,4848,4851,4854,4857,4860],{"className":4841},[70],[28,4843],{"className":4844,"style":349},[74],[28,4846,110],{"className":4847},[79,80],[28,4849,269],{"className":4850},[356],[28,4852,195],{"className":4853},[79,80],[28,4855],{"className":4856,"style":363},[89],[28,4858,3201],{"className":4859},[367],[28,4861],{"className":4862,"style":363},[89],[28,4864,4866,4869,4872,4875,4878,4881],{"className":4865},[70],[28,4867],{"className":4868,"style":349},[74],[28,4870,200],{"className":4871},[79,80],[28,4873,279],{"className":4874},[383],[28,4876],{"className":4877,"style":140},[89],[28,4879,203],{"className":4880},[144],[28,4882],{"className":4883,"style":140},[89],[28,4885,4887,4890,4896,4899,4902],{"className":4886},[70],[28,4888],{"className":4889,"style":133},[74],[28,4891,4893],{"className":4892},[1385],[28,4894,1864],{"className":4895},[79,1389],[28,4897],{"className":4898,"style":90},[89],[28,4900,110],{"className":4901},[79,80],[28,4903,336],{"className":4904},[79],[545,4906,4907,4910,4911,4203,5081,1432,5122,5150,5151,537],{},[23,4908,4909],{},"乘法封闭",":\n",[28,4912,4914,4970],{"className":4913},[31],[28,4915,4917],{"className":4916},[35],[37,4918,4919],{"xmlns":39},[41,4920,4921,4967],{},[44,4922,4923,4925,4927,4929,4931,4933,4935,4937,4939,4941,4943,4945,4947,4949,4951,4953,4955,4957,4959,4961,4963,4965],{},[47,4924,4430],{},[47,4926,4435],{},[51,4928,282],{},[47,4930,110],{},[51,4932,269],{"stretchy":268},[47,4934,195],{},[51,4936,279],{"stretchy":268},[47,4938,110],{},[51,4940,269],{"stretchy":268},[47,4942,200],{},[51,4944,279],{"stretchy":268},[51,4946,282],{},[47,4948,110],{},[51,4950,269],{"stretchy":268},[47,4952,195],{},[47,4954,200],{},[51,4956,279],{"stretchy":268},[51,4958,203],{},[47,4960,1864],{"mathvariant":191},[51,4962,1363],{},[47,4964,110],{},[47,4966,336],{"mathvariant":191},[59,4968,4969],{"encoding":61},"xy = \\phi(a)\\phi(b) = \\phi(ab) \\in \\operatorname{Im} \\phi.",[28,4971,4973,4994,5033,5060],{"className":4972,"ariaHidden":53},[66],[28,4974,4976,4979,4982,4985,4988,4991],{"className":4975},[70],[28,4977],{"className":4978,"style":4772},[74],[28,4980,4430],{"className":4981},[79,80],[28,4983,4435],{"className":4984,"style":4471},[79,80],[28,4986],{"className":4987,"style":140},[89],[28,4989,282],{"className":4990},[144],[28,4992],{"className":4993,"style":140},[89],[28,4995,4997,5000,5003,5006,5009,5012,5015,5018,5021,5024,5027,5030],{"className":4996},[70],[28,4998],{"className":4999,"style":349},[74],[28,5001,110],{"className":5002},[79,80],[28,5004,269],{"className":5005},[356],[28,5007,195],{"className":5008},[79,80],[28,5010,279],{"className":5011},[383],[28,5013,110],{"className":5014},[79,80],[28,5016,269],{"className":5017},[356],[28,5019,200],{"className":5020},[79,80],[28,5022,279],{"className":5023},[383],[28,5025],{"className":5026,"style":140},[89],[28,5028,282],{"className":5029},[144],[28,5031],{"className":5032,"style":140},[89],[28,5034,5036,5039,5042,5045,5048,5051,5054,5057],{"className":5035},[70],[28,5037],{"className":5038,"style":349},[74],[28,5040,110],{"className":5041},[79,80],[28,5043,269],{"className":5044},[356],[28,5046,457],{"className":5047},[79,80],[28,5049,279],{"className":5050},[383],[28,5052],{"className":5053,"style":140},[89],[28,5055,203],{"className":5056},[144],[28,5058],{"className":5059,"style":140},[89],[28,5061,5063,5066,5072,5075,5078],{"className":5062},[70],[28,5064],{"className":5065,"style":133},[74],[28,5067,5069],{"className":5068},[1385],[28,5070,1864],{"className":5071},[79,1389],[28,5073],{"className":5074,"style":90},[89],[28,5076,110],{"className":5077},[79,80],[28,5079,336],{"className":5080},[79],[28,5082,5084,5101],{"className":5083},[31],[28,5085,5087],{"className":5086},[35],[37,5088,5089],{"xmlns":39},[41,5090,5091,5099],{},[44,5092,5093,5095,5097],{},[47,5094,1864],{"mathvariant":191},[51,5096,1363],{},[47,5098,110],{},[59,5100,4356],{"encoding":61},[28,5102,5104],{"className":5103,"ariaHidden":53},[66],[28,5105,5107,5110,5116,5119],{"className":5106},[70],[28,5108],{"className":5109,"style":133},[74],[28,5111,5113],{"className":5112},[1385],[28,5114,1864],{"className":5115},[79,1389],[28,5117],{"className":5118,"style":90},[89],[28,5120,110],{"className":5121},[79,80],[28,5123,5125,5138],{"className":5124},[31],[28,5126,5128],{"className":5127},[35],[37,5129,5130],{"xmlns":39},[41,5131,5132,5136],{},[44,5133,5134],{},[47,5135,57],{},[59,5137,57],{"encoding":61},[28,5139,5141],{"className":5140,"ariaHidden":53},[66],[28,5142,5144,5147],{"className":5143},[70],[28,5145],{"className":5146,"style":154},[74],[28,5148,57],{"className":5149,"style":94},[79,80]," 的子环，即 ",[28,5152,5154,5175],{"className":5153},[31],[28,5155,5157],{"className":5156},[35],[37,5158,5159],{"xmlns":39},[41,5160,5161,5173],{},[44,5162,5163,5165,5167,5169,5171],{},[47,5164,1864],{"mathvariant":191},[51,5166,1363],{},[47,5168,110],{},[51,5170,2183],{},[47,5172,57],{},[59,5174,2188],{"encoding":61},[28,5176,5178,5205],{"className":5177,"ariaHidden":53},[66],[28,5179,5181,5184,5190,5193,5196,5199,5202],{"className":5180},[70],[28,5182],{"className":5183,"style":133},[74],[28,5185,5187],{"className":5186},[1385],[28,5188,1864],{"className":5189},[79,1389],[28,5191],{"className":5192,"style":90},[89],[28,5194,110],{"className":5195},[79,80],[28,5197],{"className":5198,"style":140},[89],[28,5200,2183],{"className":5201},[144],[28,5203],{"className":5204,"style":140},[89],[28,5206,5208,5211],{"className":5207},[70],[28,5209],{"className":5210,"style":154},[74],[28,5212,57],{"className":5213,"style":94},[79,80],[20,5215,5216],{},[23,5217,5218,5219,5247,5248],{},"(ii) 证明 ",[28,5220,5222,5235],{"className":5221},[31],[28,5223,5225],{"className":5224},[35],[37,5226,5227],{"xmlns":39},[41,5228,5229,5233],{},[44,5230,5231],{},[47,5232,110],{},[59,5234,520],{"encoding":61},[28,5236,5238],{"className":5237,"ariaHidden":53},[66],[28,5239,5241,5244],{"className":5240},[70],[28,5242],{"className":5243,"style":133},[74],[28,5245,110],{"className":5246},[79,80]," 是单射 ",[28,5249,5251,5284],{"className":5250},[31],[28,5252,5254],{"className":5253},[35],[37,5255,5256],{"xmlns":39},[41,5257,5258,5281],{},[44,5259,5260,5262,5265,5267,5269,5271,5273,5275,5277,5279],{},[3239,5261,3241],{},[51,5263,5264],{},"⟺",[3239,5266,3241],{},[47,5268,1701],{},[51,5270,1363],{},[47,5272,110],{},[51,5274,282],{},[51,5276,1710],{"stretchy":268},[1731,5278,1733],{},[51,5280,1736],{"stretchy":268},[59,5282,5283],{"encoding":61},"\\iff \\ker \\phi = \\{0\\}",[28,5285,5287,5306,5330],{"className":5286,"ariaHidden":53},[66],[28,5288,5290,5294,5297,5300,5303],{"className":5289},[70],[28,5291],{"className":5292,"style":5293},[74],"height:0.549em;vertical-align:-0.024em;",[28,5295],{"className":5296,"style":140},[89],[28,5298,5264],{"className":5299},[144],[28,5301],{"className":5302,"style":140},[89],[28,5304],{"className":5305,"style":140},[89],[28,5307,5309,5312,5315,5318,5321,5324,5327],{"className":5308},[70],[28,5310],{"className":5311,"style":133},[74],[28,5313,1701],{"className":5314},[1385],[28,5316],{"className":5317,"style":90},[89],[28,5319,110],{"className":5320},[79,80],[28,5322],{"className":5323,"style":140},[89],[28,5325,282],{"className":5326},[144],[28,5328],{"className":5329,"style":140},[89],[28,5331,5333,5336,5339,5342],{"className":5332},[70],[28,5334],{"className":5335,"style":349},[74],[28,5337,1710],{"className":5338},[356],[28,5340,1733],{"className":5341},[79],[28,5343,1736],{"className":5344},[383],[1679,5346,5347,5765],{},[545,5348,269,5349,5380,5381,5409,5410,5476,5477,5538,5539,5642,5643,5694,5695,537],{},[28,5350,5352,5367],{"className":5351},[31],[28,5353,5355],{"className":5354},[35],[37,5356,5357],{"xmlns":39},[41,5358,5359,5364],{},[44,5360,5361],{},[51,5362,5363],{},"⇒",[59,5365,5366],{"encoding":61},"\\Rightarrow",[28,5368,5370],{"className":5369,"ariaHidden":53},[66],[28,5371,5373,5377],{"className":5372},[70],[28,5374],{"className":5375,"style":5376},[74],"height:0.3669em;",[28,5378,5363],{"className":5379},[144],") 设 ",[28,5382,5384,5397],{"className":5383},[31],[28,5385,5387],{"className":5386},[35],[37,5388,5389],{"xmlns":39},[41,5390,5391,5395],{},[44,5392,5393],{},[47,5394,110],{},[59,5396,520],{"encoding":61},[28,5398,5400],{"className":5399,"ariaHidden":53},[66],[28,5401,5403,5406],{"className":5402},[70],[28,5404],{"className":5405,"style":133},[74],[28,5407,110],{"className":5408},[79,80]," 是单射。已知 ",[28,5411,5413,5437],{"className":5412},[31],[28,5414,5416],{"className":5415},[35],[37,5417,5418],{"xmlns":39},[41,5419,5420,5434],{},[44,5421,5422,5424,5426,5428,5430,5432],{},[47,5423,110],{},[51,5425,269],{"stretchy":268},[1731,5427,1733],{},[51,5429,279],{"stretchy":268},[51,5431,282],{},[1731,5433,1733],{},[59,5435,5436],{"encoding":61},"\\phi(0)=0",[28,5438,5440,5467],{"className":5439,"ariaHidden":53},[66],[28,5441,5443,5446,5449,5452,5455,5458,5461,5464],{"className":5442},[70],[28,5444],{"className":5445,"style":349},[74],[28,5447,110],{"className":5448},[79,80],[28,5450,269],{"className":5451},[356],[28,5453,1733],{"className":5454},[79],[28,5456,279],{"className":5457},[383],[28,5459],{"className":5460,"style":140},[89],[28,5462,282],{"className":5463},[144],[28,5465],{"className":5466,"style":140},[89],[28,5468,5470,5473],{"className":5469},[70],[28,5471],{"className":5472,"style":3176},[74],[28,5474,1733],{"className":5475},[79],"。若 ",[28,5478,5480,5502],{"className":5479},[31],[28,5481,5483],{"className":5482},[35],[37,5484,5485],{"xmlns":39},[41,5486,5487,5499],{},[44,5488,5489,5491,5493,5495,5497],{},[47,5490,195],{},[51,5492,203],{},[47,5494,1701],{},[51,5496,1363],{},[47,5498,110],{},[59,5500,5501],{"encoding":61},"a \\in \\ker \\phi",[28,5503,5505,5523],{"className":5504,"ariaHidden":53},[66],[28,5506,5508,5511,5514,5517,5520],{"className":5507},[70],[28,5509],{"className":5510,"style":1960},[74],[28,5512,195],{"className":5513},[79,80],[28,5515],{"className":5516,"style":140},[89],[28,5518,203],{"className":5519},[144],[28,5521],{"className":5522,"style":140},[89],[28,5524,5526,5529,5532,5535],{"className":5525},[70],[28,5527],{"className":5528,"style":133},[74],[28,5530,1701],{"className":5531},[1385],[28,5533],{"className":5534,"style":90},[89],[28,5536,110],{"className":5537},[79,80],"，则 ",[28,5540,5542,5576],{"className":5541},[31],[28,5543,5545],{"className":5544},[35],[37,5546,5547],{"xmlns":39},[41,5548,5549,5573],{},[44,5550,5551,5553,5555,5557,5559,5561,5563,5565,5567,5569,5571],{},[47,5552,110],{},[51,5554,269],{"stretchy":268},[47,5556,195],{},[51,5558,279],{"stretchy":268},[51,5560,282],{},[1731,5562,1733],{},[51,5564,282],{},[47,5566,110],{},[51,5568,269],{"stretchy":268},[1731,5570,1733],{},[51,5572,279],{"stretchy":268},[59,5574,5575],{"encoding":61},"\\phi(a)=0=\\phi(0)",[28,5577,5579,5606,5624],{"className":5578,"ariaHidden":53},[66],[28,5580,5582,5585,5588,5591,5594,5597,5600,5603],{"className":5581},[70],[28,5583],{"className":5584,"style":349},[74],[28,5586,110],{"className":5587},[79,80],[28,5589,269],{"className":5590},[356],[28,5592,195],{"className":5593},[79,80],[28,5595,279],{"className":5596},[383],[28,5598],{"className":5599,"style":140},[89],[28,5601,282],{"className":5602},[144],[28,5604],{"className":5605,"style":140},[89],[28,5607,5609,5612,5615,5618,5621],{"className":5608},[70],[28,5610],{"className":5611,"style":3176},[74],[28,5613,1733],{"className":5614},[79],[28,5616],{"className":5617,"style":140},[89],[28,5619,282],{"className":5620},[144],[28,5622],{"className":5623,"style":140},[89],[28,5625,5627,5630,5633,5636,5639],{"className":5626},[70],[28,5628],{"className":5629,"style":349},[74],[28,5631,110],{"className":5632},[79,80],[28,5634,269],{"className":5635},[356],[28,5637,1733],{"className":5638},[79],[28,5640,279],{"className":5641},[383],"。由单射定义知 ",[28,5644,5646,5664],{"className":5645},[31],[28,5647,5649],{"className":5648},[35],[37,5650,5651],{"xmlns":39},[41,5652,5653,5661],{},[44,5654,5655,5657,5659],{},[47,5656,195],{},[51,5658,282],{},[1731,5660,1733],{},[59,5662,5663],{"encoding":61},"a=0",[28,5665,5667,5685],{"className":5666,"ariaHidden":53},[66],[28,5668,5670,5673,5676,5679,5682],{"className":5669},[70],[28,5671],{"className":5672,"style":761},[74],[28,5674,195],{"className":5675},[79,80],[28,5677],{"className":5678,"style":140},[89],[28,5680,282],{"className":5681},[144],[28,5683],{"className":5684,"style":140},[89],[28,5686,5688,5691],{"className":5687},[70],[28,5689],{"className":5690,"style":3176},[74],[28,5692,1733],{"className":5693},[79],"。故 ",[28,5696,5698,5723],{"className":5697},[31],[28,5699,5701],{"className":5700},[35],[37,5702,5703],{"xmlns":39},[41,5704,5705,5721],{},[44,5706,5707,5709,5711,5713,5715,5717,5719],{},[47,5708,1701],{},[51,5710,1363],{},[47,5712,110],{},[51,5714,282],{},[51,5716,1710],{"stretchy":268},[1731,5718,1733],{},[51,5720,1736],{"stretchy":268},[59,5722,2315],{"encoding":61},[28,5724,5726,5750],{"className":5725,"ariaHidden":53},[66],[28,5727,5729,5732,5735,5738,5741,5744,5747],{"className":5728},[70],[28,5730],{"className":5731,"style":133},[74],[28,5733,1701],{"className":5734},[1385],[28,5736],{"className":5737,"style":90},[89],[28,5739,110],{"className":5740},[79,80],[28,5742],{"className":5743,"style":140},[89],[28,5745,282],{"className":5746},[144],[28,5748],{"className":5749,"style":140},[89],[28,5751,5753,5756,5759,5762],{"className":5752},[70],[28,5754],{"className":5755,"style":349},[74],[28,5757,1710],{"className":5758},[356],[28,5760,1733],{"className":5761},[79],[28,5763,1736],{"className":5764},[383],[545,5766,269,5767,5380,5797,5476,5867,176,5935,6015,6016,6211,6212,6295,6296,2770,6366,2873,6439,5694,6489,6517,6518],{},[28,5768,5770,5785],{"className":5769},[31],[28,5771,5773],{"className":5772},[35],[37,5774,5775],{"xmlns":39},[41,5776,5777,5782],{},[44,5778,5779],{},[51,5780,5781],{},"⇐",[59,5783,5784],{"encoding":61},"\\Leftarrow",[28,5786,5788],{"className":5787,"ariaHidden":53},[66],[28,5789,5791,5794],{"className":5790},[70],[28,5792],{"className":5793,"style":5376},[74],[28,5795,5781],{"className":5796},[144],[28,5798,5800,5825],{"className":5799},[31],[28,5801,5803],{"className":5802},[35],[37,5804,5805],{"xmlns":39},[41,5806,5807,5823],{},[44,5808,5809,5811,5813,5815,5817,5819,5821],{},[47,5810,1701],{},[51,5812,1363],{},[47,5814,110],{},[51,5816,282],{},[51,5818,1710],{"stretchy":268},[1731,5820,1733],{},[51,5822,1736],{"stretchy":268},[59,5824,2315],{"encoding":61},[28,5826,5828,5852],{"className":5827,"ariaHidden":53},[66],[28,5829,5831,5834,5837,5840,5843,5846,5849],{"className":5830},[70],[28,5832],{"className":5833,"style":133},[74],[28,5835,1701],{"className":5836},[1385],[28,5838],{"className":5839,"style":90},[89],[28,5841,110],{"className":5842},[79,80],[28,5844],{"className":5845,"style":140},[89],[28,5847,282],{"className":5848},[144],[28,5850],{"className":5851,"style":140},[89],[28,5853,5855,5858,5861,5864],{"className":5854},[70],[28,5856],{"className":5857,"style":349},[74],[28,5859,1710],{"className":5860},[356],[28,5862,1733],{"className":5863},[79],[28,5865,1736],{"className":5866},[383],[28,5868,5870,5893],{"className":5869},[31],[28,5871,5873],{"className":5872},[35],[37,5874,5875],{"xmlns":39},[41,5876,5877,5891],{},[44,5878,5879,5881,5883,5885,5887,5889],{},[47,5880,192],{"mathvariant":191},[47,5882,195],{},[51,5884,54],{"separator":53},[47,5886,200],{},[51,5888,203],{},[47,5890,49],{},[59,5892,208],{"encoding":61},[28,5894,5896,5926],{"className":5895,"ariaHidden":53},[66],[28,5897,5899,5902,5905,5908,5911,5914,5917,5920,5923],{"className":5898},[70],[28,5900],{"className":5901,"style":133},[74],[28,5903,192],{"className":5904},[79],[28,5906,195],{"className":5907},[79,80],[28,5909,54],{"className":5910},[85],[28,5912],{"className":5913,"style":90},[89],[28,5915,200],{"className":5916},[79,80],[28,5918],{"className":5919,"style":140},[89],[28,5921,203],{"className":5922},[144],[28,5924],{"className":5925,"style":140},[89],[28,5927,5929,5932],{"className":5928},[70],[28,5930],{"className":5931,"style":154},[74],[28,5933,49],{"className":5934,"style":81},[79,80],[28,5936,5938,5967],{"className":5937},[31],[28,5939,5941],{"className":5940},[35],[37,5942,5943],{"xmlns":39},[41,5944,5945,5965],{},[44,5946,5947,5949,5951,5953,5955,5957,5959,5961,5963],{},[47,5948,110],{},[51,5950,269],{"stretchy":268},[47,5952,195],{},[51,5954,279],{"stretchy":268},[51,5956,282],{},[47,5958,110],{},[51,5960,269],{"stretchy":268},[47,5962,200],{},[51,5964,279],{"stretchy":268},[59,5966,681],{"encoding":61},[28,5968,5970,5997],{"className":5969,"ariaHidden":53},[66],[28,5971,5973,5976,5979,5982,5985,5988,5991,5994],{"className":5972},[70],[28,5974],{"className":5975,"style":349},[74],[28,5977,110],{"className":5978},[79,80],[28,5980,269],{"className":5981},[356],[28,5983,195],{"className":5984},[79,80],[28,5986,279],{"className":5987},[383],[28,5989],{"className":5990,"style":140},[89],[28,5992,282],{"className":5993},[144],[28,5995],{"className":5996,"style":140},[89],[28,5998,6000,6003,6006,6009,6012],{"className":5999},[70],[28,6001],{"className":6002,"style":349},[74],[28,6004,110],{"className":6005},[79,80],[28,6007,269],{"className":6008},[356],[28,6010,200],{"className":6011},[79,80],[28,6013,279],{"className":6014},[383],"，则：\n",[28,6017,6019,6076],{"className":6018},[31],[28,6020,6022],{"className":6021},[35],[37,6023,6024],{"xmlns":39},[41,6025,6026,6073],{},[44,6027,6028,6030,6032,6034,6036,6038,6040,6042,6044,6046,6048,6050,6052,6054,6056,6058,6060,6062,6064,6066,6068,6070],{},[47,6029,110],{},[51,6031,269],{"stretchy":268},[47,6033,195],{},[51,6035,279],{"stretchy":268},[51,6037,3201],{},[47,6039,110],{},[51,6041,269],{"stretchy":268},[47,6043,200],{},[51,6045,279],{"stretchy":268},[51,6047,282],{},[1731,6049,1733],{},[3239,6051,3241],{},[51,6053,3244],{},[3239,6055,3241],{},[47,6057,110],{},[51,6059,269],{"stretchy":268},[47,6061,195],{},[51,6063,3201],{},[47,6065,200],{},[51,6067,279],{"stretchy":268},[51,6069,282],{},[1731,6071,6072],{},"0.",[59,6074,6075],{"encoding":61},"\\phi(a) - \\phi(b) = 0 \\implies \\phi(a-b) = 0.",[28,6077,6079,6106,6133,6157,6181,6202],{"className":6078,"ariaHidden":53},[66],[28,6080,6082,6085,6088,6091,6094,6097,6100,6103],{"className":6081},[70],[28,6083],{"className":6084,"style":349},[74],[28,6086,110],{"className":6087},[79,80],[28,6089,269],{"className":6090},[356],[28,6092,195],{"className":6093},[79,80],[28,6095,279],{"className":6096},[383],[28,6098],{"className":6099,"style":363},[89],[28,6101,3201],{"className":6102},[367],[28,6104],{"className":6105,"style":363},[89],[28,6107,6109,6112,6115,6118,6121,6124,6127,6130],{"className":6108},[70],[28,6110],{"className":6111,"style":349},[74],[28,6113,110],{"className":6114},[79,80],[28,6116,269],{"className":6117},[356],[28,6119,200],{"className":6120},[79,80],[28,6122,279],{"className":6123},[383],[28,6125],{"className":6126,"style":140},[89],[28,6128,282],{"className":6129},[144],[28,6131],{"className":6132,"style":140},[89],[28,6134,6136,6139,6142,6145,6148,6151,6154],{"className":6135},[70],[28,6137],{"className":6138,"style":3411},[74],[28,6140,1733],{"className":6141},[79],[28,6143],{"className":6144,"style":140},[89],[28,6146],{"className":6147,"style":140},[89],[28,6149,3244],{"className":6150},[144],[28,6152],{"className":6153,"style":140},[89],[28,6155],{"className":6156,"style":140},[89],[28,6158,6160,6163,6166,6169,6172,6175,6178],{"className":6159},[70],[28,6161],{"className":6162,"style":349},[74],[28,6164,110],{"className":6165},[79,80],[28,6167,269],{"className":6168},[356],[28,6170,195],{"className":6171},[79,80],[28,6173],{"className":6174,"style":363},[89],[28,6176,3201],{"className":6177},[367],[28,6179],{"className":6180,"style":363},[89],[28,6182,6184,6187,6190,6193,6196,6199],{"className":6183},[70],[28,6185],{"className":6186,"style":349},[74],[28,6188,200],{"className":6189},[79,80],[28,6191,279],{"className":6192},[383],[28,6194],{"className":6195,"style":140},[89],[28,6197,282],{"className":6198},[144],[28,6200],{"className":6201,"style":140},[89],[28,6203,6205,6208],{"className":6204},[70],[28,6206],{"className":6207,"style":3176},[74],[28,6209,6072],{"className":6210},[79],"\n这意味着 ",[28,6213,6215,6241],{"className":6214},[31],[28,6216,6218],{"className":6217},[35],[37,6219,6220],{"xmlns":39},[41,6221,6222,6238],{},[44,6223,6224,6226,6228,6230,6232,6234,6236],{},[47,6225,195],{},[51,6227,3201],{},[47,6229,200],{},[51,6231,203],{},[47,6233,1701],{},[51,6235,1363],{},[47,6237,110],{},[59,6239,6240],{"encoding":61},"a-b \\in \\ker \\phi",[28,6242,6244,6262,6280],{"className":6243,"ariaHidden":53},[66],[28,6245,6247,6250,6253,6256,6259],{"className":6246},[70],[28,6248],{"className":6249,"style":3436},[74],[28,6251,195],{"className":6252},[79,80],[28,6254],{"className":6255,"style":363},[89],[28,6257,3201],{"className":6258},[367],[28,6260],{"className":6261,"style":363},[89],[28,6263,6265,6268,6271,6274,6277],{"className":6264},[70],[28,6266],{"className":6267,"style":893},[74],[28,6269,200],{"className":6270},[79,80],[28,6272],{"className":6273,"style":140},[89],[28,6275,203],{"className":6276},[144],[28,6278],{"className":6279,"style":140},[89],[28,6281,6283,6286,6289,6292],{"className":6282},[70],[28,6284],{"className":6285,"style":133},[74],[28,6287,1701],{"className":6288},[1385],[28,6290],{"className":6291,"style":90},[89],[28,6293,110],{"className":6294},[79,80],"。因为 ",[28,6297,6299,6324],{"className":6298},[31],[28,6300,6302],{"className":6301},[35],[37,6303,6304],{"xmlns":39},[41,6305,6306,6322],{},[44,6307,6308,6310,6312,6314,6316,6318,6320],{},[47,6309,1701],{},[51,6311,1363],{},[47,6313,110],{},[51,6315,282],{},[51,6317,1710],{"stretchy":268},[1731,6319,1733],{},[51,6321,1736],{"stretchy":268},[59,6323,2315],{"encoding":61},[28,6325,6327,6351],{"className":6326,"ariaHidden":53},[66],[28,6328,6330,6333,6336,6339,6342,6345,6348],{"className":6329},[70],[28,6331],{"className":6332,"style":133},[74],[28,6334,1701],{"className":6335},[1385],[28,6337],{"className":6338,"style":90},[89],[28,6340,110],{"className":6341},[79,80],[28,6343],{"className":6344,"style":140},[89],[28,6346,282],{"className":6347},[144],[28,6349],{"className":6350,"style":140},[89],[28,6352,6354,6357,6360,6363],{"className":6353},[70],[28,6355],{"className":6356,"style":349},[74],[28,6358,1710],{"className":6359},[356],[28,6361,1733],{"className":6362},[79],[28,6364,1736],{"className":6365},[383],[28,6367,6369,6391],{"className":6368},[31],[28,6370,6372],{"className":6371},[35],[37,6373,6374],{"xmlns":39},[41,6375,6376,6388],{},[44,6377,6378,6380,6382,6384,6386],{},[47,6379,195],{},[51,6381,3201],{},[47,6383,200],{},[51,6385,282],{},[1731,6387,1733],{},[59,6389,6390],{"encoding":61},"a-b=0",[28,6392,6394,6412,6430],{"className":6393,"ariaHidden":53},[66],[28,6395,6397,6400,6403,6406,6409],{"className":6396},[70],[28,6398],{"className":6399,"style":3436},[74],[28,6401,195],{"className":6402},[79,80],[28,6404],{"className":6405,"style":363},[89],[28,6407,3201],{"className":6408},[367],[28,6410],{"className":6411,"style":363},[89],[28,6413,6415,6418,6421,6424,6427],{"className":6414},[70],[28,6416],{"className":6417,"style":780},[74],[28,6419,200],{"className":6420},[79,80],[28,6422],{"className":6423,"style":140},[89],[28,6425,282],{"className":6426},[144],[28,6428],{"className":6429,"style":140},[89],[28,6431,6433,6436],{"className":6432},[70],[28,6434],{"className":6435,"style":3176},[74],[28,6437,1733],{"className":6438},[79],[28,6440,6442,6459],{"className":6441},[31],[28,6443,6445],{"className":6444},[35],[37,6446,6447],{"xmlns":39},[41,6448,6449,6457],{},[44,6450,6451,6453,6455],{},[47,6452,195],{},[51,6454,282],{},[47,6456,200],{},[59,6458,751],{"encoding":61},[28,6460,6462,6480],{"className":6461,"ariaHidden":53},[66],[28,6463,6465,6468,6471,6474,6477],{"className":6464},[70],[28,6466],{"className":6467,"style":761},[74],[28,6469,195],{"className":6470},[79,80],[28,6472],{"className":6473,"style":140},[89],[28,6475,282],{"className":6476},[144],[28,6478],{"className":6479,"style":140},[89],[28,6481,6483,6486],{"className":6482},[70],[28,6484],{"className":6485,"style":780},[74],[28,6487,200],{"className":6488},[79,80],[28,6490,6492,6505],{"className":6491},[31],[28,6493,6495],{"className":6494},[35],[37,6496,6497],{"xmlns":39},[41,6498,6499,6503],{},[44,6500,6501],{},[47,6502,110],{},[59,6504,520],{"encoding":61},[28,6506,6508],{"className":6507,"ariaHidden":53},[66],[28,6509,6511,6514],{"className":6510},[70],[28,6512],{"className":6513,"style":133},[74],[28,6515,110],{"className":6516},[79,80]," 是单射。 ",[28,6519,6521,6536],{"className":6520},[31],[28,6522,6524],{"className":6523},[35],[37,6525,6526],{"xmlns":39},[41,6527,6528,6533],{},[44,6529,6530],{},[47,6531,6532],{"mathvariant":191},"□",[59,6534,6535],{"encoding":61},"\\square",[28,6537,6539],{"className":6538,"ariaHidden":53},[66],[28,6540,6542,6546],{"className":6541},[70],[28,6543],{"className":6544,"style":6545},[74],"height:0.675em;",[28,6547,6532],{"className":6548},[79,2120],[20,6550,6551,6554,6555,6627,6628,6682,6683,6907,6908,6911,6912,7071,7072,7473,7474,7580,7581],{},[23,6552,6553],{},"命题 3.3.2."," ",[28,6556,6558,6579],{"className":6557},[31],[28,6559,6561],{"className":6560},[35],[37,6562,6563],{"xmlns":39},[41,6564,6565,6577],{},[44,6566,6567,6569,6571,6573,6575],{},[47,6568,110],{},[51,6570,113],{},[47,6572,49],{},[51,6574,118],{},[47,6576,57],{},[59,6578,123],{"encoding":61},[28,6580,6582,6600,6618],{"className":6581,"ariaHidden":53},[66],[28,6583,6585,6588,6591,6594,6597],{"className":6584},[70],[28,6586],{"className":6587,"style":133},[74],[28,6589,110],{"className":6590},[79,80],[28,6592],{"className":6593,"style":140},[89],[28,6595,113],{"className":6596},[144],[28,6598],{"className":6599,"style":140},[89],[28,6601,6603,6606,6609,6612,6615],{"className":6602},[70],[28,6604],{"className":6605,"style":154},[74],[28,6607,49],{"className":6608,"style":81},[79,80],[28,6610],{"className":6611,"style":140},[89],[28,6613,118],{"className":6614},[144],[28,6616],{"className":6617,"style":140},[89],[28,6619,6621,6624],{"className":6620},[70],[28,6622],{"className":6623,"style":154},[74],[28,6625,57],{"className":6626,"style":94},[79,80]," 是一个环同态， ",[28,6629,6631,6650],{"className":6630},[31],[28,6632,6634],{"className":6633},[35],[37,6635,6636],{"xmlns":39},[41,6637,6638,6647],{},[44,6639,6640,6643,6645],{},[47,6641,6642],{},"J",[51,6644,2090],{},[47,6646,57],{},[59,6648,6649],{"encoding":61},"J \\lhd S",[28,6651,6653,6673],{"className":6652,"ariaHidden":53},[66],[28,6654,6656,6660,6664,6667,6670],{"className":6655},[70],[28,6657],{"className":6658,"style":6659},[74],"height:0.7185em;vertical-align:-0.0352em;",[28,6661,6642],{"className":6662,"style":6663},[79,80],"margin-right:0.0962em;",[28,6665],{"className":6666,"style":363},[89],[28,6668,2090],{"className":6669},[367,2120],[28,6671],{"className":6672,"style":363},[89],[28,6674,6676,6679],{"className":6675},[70],[28,6677],{"className":6678,"style":154},[74],[28,6680,57],{"className":6681,"style":94},[79,80],". 则 ",[28,6684,6686,6746],{"className":6685},[31],[28,6687,6689],{"className":6688},[35],[37,6690,6691],{"xmlns":39},[41,6692,6693,6743],{},[44,6694,6695,6707,6709,6711,6713,6715,6717,6719,6721,6723,6725,6727,6729,6731,6733,6735,6737,6739,6741],{},[6696,6697,6698,6700],"msup",{},[47,6699,110],{},[44,6701,6702,6704],{},[51,6703,3201],{},[1731,6705,6706],{},"1",[51,6708,269],{"stretchy":268},[47,6710,6642],{},[51,6712,279],{"stretchy":268},[51,6714,282],{},[51,6716,1710],{"stretchy":268},[47,6718,195],{},[51,6720,203],{},[47,6722,49],{},[51,6724,1719],{},[47,6726,110],{},[51,6728,269],{"stretchy":268},[47,6730,195],{},[51,6732,279],{"stretchy":268},[51,6734,203],{},[47,6736,6642],{},[51,6738,1736],{"stretchy":268},[51,6740,2090],{},[47,6742,49],{},[59,6744,6745],{"encoding":61},"\\phi^{-1}(J) = \\{a \\in R \\mid \\phi(a) \\in J\\} \\lhd R",[28,6747,6749,6811,6832,6850,6877,6898],{"className":6748,"ariaHidden":53},[66],[28,6750,6752,6756,6793,6796,6799,6802,6805,6808],{"className":6751},[70],[28,6753],{"className":6754,"style":6755},[74],"height:1.0641em;vertical-align:-0.25em;",[28,6757,6759,6762],{"className":6758},[79],[28,6760,110],{"className":6761},[79,80],[28,6763,6765],{"className":6764},[2664],[28,6766,6768],{"className":6767},[2668],[28,6769,6771],{"className":6770},[2673],[28,6772,6775],{"className":6773,"style":6774},[2677],"height:0.8141em;",[28,6776,6778,6781],{"style":6777},"top:-3.063em;margin-right:0.05em;",[28,6779],{"className":6780,"style":2686},[2685],[28,6782,6784],{"className":6783},[2690,2691,2692,2693],[28,6785,6787,6790],{"className":6786},[79,2693],[28,6788,3201],{"className":6789},[79,2693],[28,6791,6706],{"className":6792},[79,2693],[28,6794,269],{"className":6795},[356],[28,6797,6642],{"className":6798,"style":6663},[79,80],[28,6800,279],{"className":6801},[383],[28,6803],{"className":6804,"style":140},[89],[28,6806,282],{"className":6807},[144],[28,6809],{"className":6810,"style":140},[89],[28,6812,6814,6817,6820,6823,6826,6829],{"className":6813},[70],[28,6815],{"className":6816,"style":349},[74],[28,6818,1710],{"className":6819},[356],[28,6821,195],{"className":6822},[79,80],[28,6824],{"className":6825,"style":140},[89],[28,6827,203],{"className":6828},[144],[28,6830],{"className":6831,"style":140},[89],[28,6833,6835,6838,6841,6844,6847],{"className":6834},[70],[28,6836],{"className":6837,"style":349},[74],[28,6839,49],{"className":6840,"style":81},[79,80],[28,6842],{"className":6843,"style":140},[89],[28,6845,1719],{"className":6846},[144],[28,6848],{"className":6849,"style":140},[89],[28,6851,6853,6856,6859,6862,6865,6868,6871,6874],{"className":6852},[70],[28,6854],{"className":6855,"style":349},[74],[28,6857,110],{"className":6858},[79,80],[28,6860,269],{"className":6861},[356],[28,6863,195],{"className":6864},[79,80],[28,6866,279],{"className":6867},[383],[28,6869],{"className":6870,"style":140},[89],[28,6872,203],{"className":6873},[144],[28,6875],{"className":6876,"style":140},[89],[28,6878,6880,6883,6886,6889,6892,6895],{"className":6879},[70],[28,6881],{"className":6882,"style":349},[74],[28,6884,6642],{"className":6885,"style":6663},[79,80],[28,6887,1736],{"className":6888},[383],[28,6890],{"className":6891,"style":363},[89],[28,6893,2090],{"className":6894},[367,2120],[28,6896],{"className":6897,"style":363},[89],[28,6899,6901,6904],{"className":6900},[70],[28,6902],{"className":6903,"style":154},[74],[28,6905,49],{"className":6906,"style":81},[79,80],".\n",[23,6909,6910],{},"证明:"," 利用命题 3.2.3, ",[28,6913,6915,6961],{"className":6914},[31],[28,6916,6918],{"className":6917},[35],[37,6919,6920],{"xmlns":39},[41,6921,6922,6958],{},[44,6923,6924,6926,6928,6930,6932,6934,6944,6946,6948,6950,6952,6954,6956],{},[47,6925,192],{"mathvariant":191},[47,6927,195],{},[51,6929,54],{"separator":53},[47,6931,200],{},[51,6933,203],{},[6696,6935,6936,6938],{},[47,6937,110],{},[44,6939,6940,6942],{},[51,6941,3201],{},[1731,6943,6706],{},[51,6945,269],{"stretchy":268},[47,6947,6642],{},[51,6949,279],{"stretchy":268},[51,6951,54],{"separator":53},[47,6953,876],{},[51,6955,203],{},[47,6957,49],{},[59,6959,6960],{"encoding":61},"\\forall a, b \\in \\phi^{-1}(J), r \\in R",[28,6962,6964,6994,7062],{"className":6963,"ariaHidden":53},[66],[28,6965,6967,6970,6973,6976,6979,6982,6985,6988,6991],{"className":6966},[70],[28,6968],{"className":6969,"style":133},[74],[28,6971,192],{"className":6972},[79],[28,6974,195],{"className":6975},[79,80],[28,6977,54],{"className":6978},[85],[28,6980],{"className":6981,"style":90},[89],[28,6983,200],{"className":6984},[79,80],[28,6986],{"className":6987,"style":140},[89],[28,6989,203],{"className":6990},[144],[28,6992],{"className":6993,"style":140},[89],[28,6995,6997,7000,7035,7038,7041,7044,7047,7050,7053,7056,7059],{"className":6996},[70],[28,6998],{"className":6999,"style":6755},[74],[28,7001,7003,7006],{"className":7002},[79],[28,7004,110],{"className":7005},[79,80],[28,7007,7009],{"className":7008},[2664],[28,7010,7012],{"className":7011},[2668],[28,7013,7015],{"className":7014},[2673],[28,7016,7018],{"className":7017,"style":6774},[2677],[28,7019,7020,7023],{"style":6777},[28,7021],{"className":7022,"style":2686},[2685],[28,7024,7026],{"className":7025},[2690,2691,2692,2693],[28,7027,7029,7032],{"className":7028},[79,2693],[28,7030,3201],{"className":7031},[79,2693],[28,7033,6706],{"className":7034},[79,2693],[28,7036,269],{"className":7037},[356],[28,7039,6642],{"className":7040,"style":6663},[79,80],[28,7042,279],{"className":7043},[383],[28,7045,54],{"className":7046},[85],[28,7048],{"className":7049,"style":90},[89],[28,7051,876],{"className":7052,"style":930},[79,80],[28,7054],{"className":7055,"style":140},[89],[28,7057,203],{"className":7058},[144],[28,7060],{"className":7061,"style":140},[89],[28,7063,7065,7068],{"className":7064},[70],[28,7066],{"className":7067,"style":154},[74],[28,7069,49],{"className":7070,"style":81},[79,80],", 都有\n",[28,7073,7075,7197],{"className":7074},[31],[28,7076,7078],{"className":7077},[35],[37,7079,7080],{"xmlns":39},[41,7081,7082,7194],{},[44,7083,7084,7086,7088,7090,7092,7094,7096,7098,7100,7102,7104,7106,7108,7110,7112,7114,7116,7118,7120,7122,7124,7126,7128,7130,7132,7134,7136,7138,7140,7142,7144,7146,7148,7150,7152,7154,7156,7158,7160,7162,7164,7166,7168,7170,7172,7174,7176,7178,7180,7182,7184,7186,7188,7190,7192],{},[47,7085,110],{},[51,7087,269],{"stretchy":268},[47,7089,195],{},[51,7091,3201],{},[47,7093,200],{},[51,7095,279],{"stretchy":268},[51,7097,282],{},[47,7099,110],{},[51,7101,269],{"stretchy":268},[47,7103,195],{},[51,7105,279],{"stretchy":268},[51,7107,3201],{},[47,7109,110],{},[51,7111,269],{"stretchy":268},[47,7113,200],{},[51,7115,279],{"stretchy":268},[51,7117,203],{},[47,7119,6642],{},[51,7121,54],{"separator":53},[89,7123],{"width":305},[47,7125,110],{},[51,7127,269],{"stretchy":268},[47,7129,876],{},[47,7131,195],{},[51,7133,279],{"stretchy":268},[51,7135,282],{},[47,7137,110],{},[51,7139,269],{"stretchy":268},[47,7141,876],{},[51,7143,279],{"stretchy":268},[47,7145,110],{},[51,7147,269],{"stretchy":268},[47,7149,195],{},[51,7151,279],{"stretchy":268},[51,7153,203],{},[47,7155,6642],{},[51,7157,54],{"separator":53},[89,7159],{"width":305},[47,7161,110],{},[51,7163,269],{"stretchy":268},[47,7165,195],{},[47,7167,876],{},[51,7169,279],{"stretchy":268},[51,7171,282],{},[47,7173,110],{},[51,7175,269],{"stretchy":268},[47,7177,195],{},[51,7179,279],{"stretchy":268},[47,7181,110],{},[51,7183,269],{"stretchy":268},[47,7185,876],{},[51,7187,279],{"stretchy":268},[51,7189,203],{},[47,7191,6642],{},[47,7193,336],{"mathvariant":191},[59,7195,7196],{"encoding":61},"\\phi(a-b) = \\phi(a) - \\phi(b) \\in J, \\quad \\phi(ra) = \\phi(r)\\phi(a) \\in J, \\quad \\phi(ar) = \\phi(a)\\phi(r) \\in J.",[28,7198,7200,7224,7245,7272,7299,7341,7380,7422,7461],{"className":7199,"ariaHidden":53},[66],[28,7201,7203,7206,7209,7212,7215,7218,7221],{"className":7202},[70],[28,7204],{"className":7205,"style":349},[74],[28,7207,110],{"className":7208},[79,80],[28,7210,269],{"className":7211},[356],[28,7213,195],{"className":7214},[79,80],[28,7216],{"className":7217,"style":363},[89],[28,7219,3201],{"className":7220},[367],[28,7222],{"className":7223,"style":363},[89],[28,7225,7227,7230,7233,7236,7239,7242],{"className":7226},[70],[28,7228],{"className":7229,"style":349},[74],[28,7231,200],{"className":7232},[79,80],[28,7234,279],{"className":7235},[383],[28,7237],{"className":7238,"style":140},[89],[28,7240,282],{"className":7241},[144],[28,7243],{"className":7244,"style":140},[89],[28,7246,7248,7251,7254,7257,7260,7263,7266,7269],{"className":7247},[70],[28,7249],{"className":7250,"style":349},[74],[28,7252,110],{"className":7253},[79,80],[28,7255,269],{"className":7256},[356],[28,7258,195],{"className":7259},[79,80],[28,7261,279],{"className":7262},[383],[28,7264],{"className":7265,"style":363},[89],[28,7267,3201],{"className":7268},[367],[28,7270],{"className":7271,"style":363},[89],[28,7273,7275,7278,7281,7284,7287,7290,7293,7296],{"className":7274},[70],[28,7276],{"className":7277,"style":349},[74],[28,7279,110],{"className":7280},[79,80],[28,7282,269],{"className":7283},[356],[28,7285,200],{"className":7286},[79,80],[28,7288,279],{"className":7289},[383],[28,7291],{"className":7292,"style":140},[89],[28,7294,203],{"className":7295},[144],[28,7297],{"className":7298,"style":140},[89],[28,7300,7302,7305,7308,7311,7314,7317,7320,7323,7326,7329,7332,7335,7338],{"className":7301},[70],[28,7303],{"className":7304,"style":349},[74],[28,7306,6642],{"className":7307,"style":6663},[79,80],[28,7309,54],{"className":7310},[85],[28,7312],{"className":7313,"style":444},[89],[28,7315],{"className":7316,"style":90},[89],[28,7318,110],{"className":7319},[79,80],[28,7321,269],{"className":7322},[356],[28,7324,876],{"className":7325,"style":930},[79,80],[28,7327,195],{"className":7328},[79,80],[28,7330,279],{"className":7331},[383],[28,7333],{"className":7334,"style":140},[89],[28,7336,282],{"className":7337},[144],[28,7339],{"className":7340,"style":140},[89],[28,7342,7344,7347,7350,7353,7356,7359,7362,7365,7368,7371,7374,7377],{"className":7343},[70],[28,7345],{"className":7346,"style":349},[74],[28,7348,110],{"className":7349},[79,80],[28,7351,269],{"className":7352},[356],[28,7354,876],{"className":7355,"style":930},[79,80],[28,7357,279],{"className":7358},[383],[28,7360,110],{"className":7361},[79,80],[28,7363,269],{"className":7364},[356],[28,7366,195],{"className":7367},[79,80],[28,7369,279],{"className":7370},[383],[28,7372],{"className":7373,"style":140},[89],[28,7375,203],{"className":7376},[144],[28,7378],{"className":7379,"style":140},[89],[28,7381,7383,7386,7389,7392,7395,7398,7401,7404,7407,7410,7413,7416,7419],{"className":7382},[70],[28,7384],{"className":7385,"style":349},[74],[28,7387,6642],{"className":7388,"style":6663},[79,80],[28,7390,54],{"className":7391},[85],[28,7393],{"className":7394,"style":444},[89],[28,7396],{"className":7397,"style":90},[89],[28,7399,110],{"className":7400},[79,80],[28,7402,269],{"className":7403},[356],[28,7405,195],{"className":7406},[79,80],[28,7408,876],{"className":7409,"style":930},[79,80],[28,7411,279],{"className":7412},[383],[28,7414],{"className":7415,"style":140},[89],[28,7417,282],{"className":7418},[144],[28,7420],{"className":7421,"style":140},[89],[28,7423,7425,7428,7431,7434,7437,7440,7443,7446,7449,7452,7455,7458],{"className":7424},[70],[28,7426],{"className":7427,"style":349},[74],[28,7429,110],{"className":7430},[79,80],[28,7432,269],{"className":7433},[356],[28,7435,195],{"className":7436},[79,80],[28,7438,279],{"className":7439},[383],[28,7441,110],{"className":7442},[79,80],[28,7444,269],{"className":7445},[356],[28,7447,876],{"className":7448,"style":930},[79,80],[28,7450,279],{"className":7451},[383],[28,7453],{"className":7454,"style":140},[89],[28,7456,203],{"className":7457},[144],[28,7459],{"className":7460,"style":140},[89],[28,7462,7464,7467,7470],{"className":7463},[70],[28,7465],{"className":7466,"style":154},[74],[28,7468,6642],{"className":7469,"style":6663},[79,80],[28,7471,336],{"className":7472},[79],"\n因此 ",[28,7475,7477,7509],{"className":7476},[31],[28,7478,7480],{"className":7479},[35],[37,7481,7482],{"xmlns":39},[41,7483,7484,7506],{},[44,7485,7486,7496,7498,7500,7502,7504],{},[6696,7487,7488,7490],{},[47,7489,110],{},[44,7491,7492,7494],{},[51,7493,3201],{},[1731,7495,6706],{},[51,7497,269],{"stretchy":268},[47,7499,6642],{},[51,7501,279],{"stretchy":268},[51,7503,2090],{},[47,7505,49],{},[59,7507,7508],{"encoding":61},"\\phi^{-1}(J) \\lhd R",[28,7510,7512,7571],{"className":7511,"ariaHidden":53},[66],[28,7513,7515,7518,7553,7556,7559,7562,7565,7568],{"className":7514},[70],[28,7516],{"className":7517,"style":6755},[74],[28,7519,7521,7524],{"className":7520},[79],[28,7522,110],{"className":7523},[79,80],[28,7525,7527],{"className":7526},[2664],[28,7528,7530],{"className":7529},[2668],[28,7531,7533],{"className":7532},[2673],[28,7534,7536],{"className":7535,"style":6774},[2677],[28,7537,7538,7541],{"style":6777},[28,7539],{"className":7540,"style":2686},[2685],[28,7542,7544],{"className":7543},[2690,2691,2692,2693],[28,7545,7547,7550],{"className":7546},[79,2693],[28,7548,3201],{"className":7549},[79,2693],[28,7551,6706],{"className":7552},[79,2693],[28,7554,269],{"className":7555},[356],[28,7557,6642],{"className":7558,"style":6663},[79,80],[28,7560,279],{"className":7561},[383],[28,7563],{"className":7564,"style":363},[89],[28,7566,2090],{"className":7567},[367,2120],[28,7569],{"className":7570,"style":363},[89],[28,7572,7574,7577],{"className":7573},[70],[28,7575],{"className":7576,"style":154},[74],[28,7578,49],{"className":7579,"style":81},[79,80],". ",[28,7582,7584,7597],{"className":7583},[31],[28,7585,7587],{"className":7586},[35],[37,7588,7589],{"xmlns":39},[41,7590,7591,7595],{},[44,7592,7593],{},[47,7594,6532],{"mathvariant":191},[59,7596,6535],{"encoding":61},[28,7598,7600],{"className":7599,"ariaHidden":53},[66],[28,7601,7603,7606],{"className":7602},[70],[28,7604],{"className":7605,"style":6545},[74],[28,7607,6532],{"className":7608},[79,2120],[1986,7610],{},[15,7612,7614],{"id":7613},"_3-环同态定理","3. 环同态定理",[20,7616,7617,26,7620,7673,7674,7759,7760,7848],{},[23,7618,7619],{},"定理 3.3.1 (典范同态).",[28,7621,7623,7642],{"className":7622},[31],[28,7624,7626],{"className":7625},[35],[37,7627,7628],{"xmlns":39},[41,7629,7630,7639],{},[44,7631,7632,7635,7637],{},[47,7633,7634],{},"I",[51,7636,2090],{},[47,7638,49],{},[59,7640,7641],{"encoding":61},"I \\lhd R",[28,7643,7645,7664],{"className":7644,"ariaHidden":53},[66],[28,7646,7648,7651,7655,7658,7661],{"className":7647},[70],[28,7649],{"className":7650,"style":6659},[74],[28,7652,7634],{"className":7653,"style":7654},[79,80],"margin-right:0.0785em;",[28,7656],{"className":7657,"style":363},[89],[28,7659,2090],{"className":7660},[367,2120],[28,7662],{"className":7663,"style":363},[89],[28,7665,7667,7670],{"className":7666},[70],[28,7668],{"className":7669,"style":154},[74],[28,7671,49],{"className":7672,"style":81},[79,80],". 则映射 ",[28,7675,7677,7705],{"className":7676},[31],[28,7678,7680],{"className":7679},[35],[37,7681,7682],{"xmlns":39},[41,7683,7684,7702],{},[44,7685,7686,7689,7691,7693,7695,7697,7700],{},[47,7687,7688],{},"π",[51,7690,113],{},[47,7692,49],{},[51,7694,118],{},[47,7696,49],{},[47,7698,7699],{"mathvariant":191},"\u002F",[47,7701,7634],{},[59,7703,7704],{"encoding":61},"\\pi: R \\to R\u002FI",[28,7706,7708,7726,7744],{"className":7707,"ariaHidden":53},[66],[28,7709,7711,7714,7717,7720,7723],{"className":7710},[70],[28,7712],{"className":7713,"style":761},[74],[28,7715,7688],{"className":7716,"style":4471},[79,80],[28,7718],{"className":7719,"style":140},[89],[28,7721,113],{"className":7722},[144],[28,7724],{"className":7725,"style":140},[89],[28,7727,7729,7732,7735,7738,7741],{"className":7728},[70],[28,7730],{"className":7731,"style":154},[74],[28,7733,49],{"className":7734,"style":81},[79,80],[28,7736],{"className":7737,"style":140},[89],[28,7739,118],{"className":7740},[144],[28,7742],{"className":7743,"style":140},[89],[28,7745,7747,7750,7753,7756],{"className":7746},[70],[28,7748],{"className":7749,"style":349},[74],[28,7751,49],{"className":7752,"style":81},[79,80],[28,7754,7699],{"className":7755},[79],[28,7757,7634],{"className":7758,"style":7654},[79,80]," 定义为 ",[28,7761,7763,7791],{"className":7762},[31],[28,7764,7766],{"className":7765},[35],[37,7767,7768],{"xmlns":39},[41,7769,7770,7788],{},[44,7771,7772,7774,7776,7778,7780,7782,7784,7786],{},[47,7773,7688],{},[51,7775,269],{"stretchy":268},[47,7777,876],{},[51,7779,279],{"stretchy":268},[51,7781,282],{},[47,7783,876],{},[51,7785,274],{},[47,7787,7634],{},[59,7789,7790],{"encoding":61},"\\pi(r) = r+I",[28,7792,7794,7821,7839],{"className":7793,"ariaHidden":53},[66],[28,7795,7797,7800,7803,7806,7809,7812,7815,7818],{"className":7796},[70],[28,7798],{"className":7799,"style":349},[74],[28,7801,7688],{"className":7802,"style":4471},[79,80],[28,7804,269],{"className":7805},[356],[28,7807,876],{"className":7808,"style":930},[79,80],[28,7810,279],{"className":7811},[383],[28,7813],{"className":7814,"style":140},[89],[28,7816,282],{"className":7817},[144],[28,7819],{"className":7820,"style":140},[89],[28,7822,7824,7827,7830,7833,7836],{"className":7823},[70],[28,7825],{"className":7826,"style":3436},[74],[28,7828,876],{"className":7829,"style":930},[79,80],[28,7831],{"className":7832,"style":363},[89],[28,7834,274],{"className":7835},[367],[28,7837],{"className":7838,"style":363},[89],[28,7840,7842,7845],{"className":7841},[70],[28,7843],{"className":7844,"style":154},[74],[28,7846,7634],{"className":7847,"style":7654},[79,80]," 是一个环同态，称为典范同态。",[20,7850,7851,7853,7854,7883,7884,7923,7924,8115,8116,537],{},[23,7852,2362],{},"\n我们需要验证 ",[28,7855,7857,7871],{"className":7856},[31],[28,7858,7860],{"className":7859},[35],[37,7861,7862],{"xmlns":39},[41,7863,7864,7868],{},[44,7865,7866],{},[47,7867,7688],{},[59,7869,7870],{"encoding":61},"\\pi",[28,7872,7874],{"className":7873,"ariaHidden":53},[66],[28,7875,7877,7880],{"className":7876},[70],[28,7878],{"className":7879,"style":761},[74],[28,7881,7688],{"className":7882,"style":4471},[79,80]," 保持加法和乘法运算。回顾商环 ",[28,7885,7887,7905],{"className":7886},[31],[28,7888,7890],{"className":7889},[35],[37,7891,7892],{"xmlns":39},[41,7893,7894,7902],{},[44,7895,7896,7898,7900],{},[47,7897,49],{},[47,7899,7699],{"mathvariant":191},[47,7901,7634],{},[59,7903,7904],{"encoding":61},"R\u002FI",[28,7906,7908],{"className":7907,"ariaHidden":53},[66],[28,7909,7911,7914,7917,7920],{"className":7910},[70],[28,7912],{"className":7913,"style":349},[74],[28,7915,49],{"className":7916,"style":81},[79,80],[28,7918,7699],{"className":7919},[79],[28,7921,7634],{"className":7922,"style":7654},[79,80]," 的运算定义：",[28,7925,7927,7977],{"className":7926},[31],[28,7928,7930],{"className":7929},[35],[37,7931,7932],{"xmlns":39},[41,7933,7934,7974],{},[44,7935,7936,7938,7940,7942,7944,7946,7948,7950,7952,7954,7956,7958,7960,7962,7964,7966,7968,7970,7972],{},[51,7937,269],{"stretchy":268},[47,7939,195],{},[51,7941,274],{},[47,7943,7634],{},[51,7945,279],{"stretchy":268},[51,7947,274],{},[51,7949,269],{"stretchy":268},[47,7951,200],{},[51,7953,274],{},[47,7955,7634],{},[51,7957,279],{"stretchy":268},[51,7959,282],{},[51,7961,269],{"stretchy":268},[47,7963,195],{},[51,7965,274],{},[47,7967,200],{},[51,7969,279],{"stretchy":268},[51,7971,274],{},[47,7973,7634],{},[59,7975,7976],{"encoding":61},"(a+I)+(b+I) = (a+b)+I",[28,7978,7980,8001,8022,8043,8064,8085,8106],{"className":7979,"ariaHidden":53},[66],[28,7981,7983,7986,7989,7992,7995,7998],{"className":7982},[70],[28,7984],{"className":7985,"style":349},[74],[28,7987,269],{"className":7988},[356],[28,7990,195],{"className":7991},[79,80],[28,7993],{"className":7994,"style":363},[89],[28,7996,274],{"className":7997},[367],[28,7999],{"className":8000,"style":363},[89],[28,8002,8004,8007,8010,8013,8016,8019],{"className":8003},[70],[28,8005],{"className":8006,"style":349},[74],[28,8008,7634],{"className":8009,"style":7654},[79,80],[28,8011,279],{"className":8012},[383],[28,8014],{"className":8015,"style":363},[89],[28,8017,274],{"className":8018},[367],[28,8020],{"className":8021,"style":363},[89],[28,8023,8025,8028,8031,8034,8037,8040],{"className":8024},[70],[28,8026],{"className":8027,"style":349},[74],[28,8029,269],{"className":8030},[356],[28,8032,200],{"className":8033},[79,80],[28,8035],{"className":8036,"style":363},[89],[28,8038,274],{"className":8039},[367],[28,8041],{"className":8042,"style":363},[89],[28,8044,8046,8049,8052,8055,8058,8061],{"className":8045},[70],[28,8047],{"className":8048,"style":349},[74],[28,8050,7634],{"className":8051,"style":7654},[79,80],[28,8053,279],{"className":8054},[383],[28,8056],{"className":8057,"style":140},[89],[28,8059,282],{"className":8060},[144],[28,8062],{"className":8063,"style":140},[89],[28,8065,8067,8070,8073,8076,8079,8082],{"className":8066},[70],[28,8068],{"className":8069,"style":349},[74],[28,8071,269],{"className":8072},[356],[28,8074,195],{"className":8075},[79,80],[28,8077],{"className":8078,"style":363},[89],[28,8080,274],{"className":8081},[367],[28,8083],{"className":8084,"style":363},[89],[28,8086,8088,8091,8094,8097,8100,8103],{"className":8087},[70],[28,8089],{"className":8090,"style":349},[74],[28,8092,200],{"className":8093},[79,80],[28,8095,279],{"className":8096},[383],[28,8098],{"className":8099,"style":363},[89],[28,8101,274],{"className":8102},[367],[28,8104],{"className":8105,"style":363},[89],[28,8107,8109,8112],{"className":8108},[70],[28,8110],{"className":8111,"style":154},[74],[28,8113,7634],{"className":8114,"style":7654},[79,80]," 以及 ",[28,8117,8119,8161],{"className":8118},[31],[28,8120,8122],{"className":8121},[35],[37,8123,8124],{"xmlns":39},[41,8125,8126,8158],{},[44,8127,8128,8130,8132,8134,8136,8138,8140,8142,8144,8146,8148,8150,8152,8154,8156],{},[51,8129,269],{"stretchy":268},[47,8131,195],{},[51,8133,274],{},[47,8135,7634],{},[51,8137,279],{"stretchy":268},[51,8139,269],{"stretchy":268},[47,8141,200],{},[51,8143,274],{},[47,8145,7634],{},[51,8147,279],{"stretchy":268},[51,8149,282],{},[47,8151,195],{},[47,8153,200],{},[51,8155,274],{},[47,8157,7634],{},[59,8159,8160],{"encoding":61},"(a+I)(b+I) = ab+I",[28,8162,8164,8185,8212,8233,8252],{"className":8163,"ariaHidden":53},[66],[28,8165,8167,8170,8173,8176,8179,8182],{"className":8166},[70],[28,8168],{"className":8169,"style":349},[74],[28,8171,269],{"className":8172},[356],[28,8174,195],{"className":8175},[79,80],[28,8177],{"className":8178,"style":363},[89],[28,8180,274],{"className":8181},[367],[28,8183],{"className":8184,"style":363},[89],[28,8186,8188,8191,8194,8197,8200,8203,8206,8209],{"className":8187},[70],[28,8189],{"className":8190,"style":349},[74],[28,8192,7634],{"className":8193,"style":7654},[79,80],[28,8195,279],{"className":8196},[383],[28,8198,269],{"className":8199},[356],[28,8201,200],{"className":8202},[79,80],[28,8204],{"className":8205,"style":363},[89],[28,8207,274],{"className":8208},[367],[28,8210],{"className":8211,"style":363},[89],[28,8213,8215,8218,8221,8224,8227,8230],{"className":8214},[70],[28,8216],{"className":8217,"style":349},[74],[28,8219,7634],{"className":8220,"style":7654},[79,80],[28,8222,279],{"className":8223},[383],[28,8225],{"className":8226,"style":140},[89],[28,8228,282],{"className":8229},[144],[28,8231],{"className":8232,"style":140},[89],[28,8234,8236,8240,8243,8246,8249],{"className":8235},[70],[28,8237],{"className":8238,"style":8239},[74],"height:0.7778em;vertical-align:-0.0833em;",[28,8241,457],{"className":8242},[79,80],[28,8244],{"className":8245,"style":363},[89],[28,8247,274],{"className":8248},[367],[28,8250],{"className":8251,"style":363},[89],[28,8253,8255,8258],{"className":8254},[70],[28,8256],{"className":8257,"style":154},[74],[28,8259,7634],{"className":8260,"style":7654},[79,80],[542,8262,8263,8666],{},[545,8264,8265,1686,8268,8336,8337],{},[23,8266,8267],{},"保持加法",[28,8269,8271,8294],{"className":8270},[31],[28,8272,8274],{"className":8273},[35],[37,8275,8276],{"xmlns":39},[41,8277,8278,8292],{},[44,8279,8280,8282,8284,8286,8288,8290],{},[47,8281,192],{"mathvariant":191},[47,8283,195],{},[51,8285,54],{"separator":53},[47,8287,200],{},[51,8289,203],{},[47,8291,49],{},[59,8293,208],{"encoding":61},[28,8295,8297,8327],{"className":8296,"ariaHidden":53},[66],[28,8298,8300,8303,8306,8309,8312,8315,8318,8321,8324],{"className":8299},[70],[28,8301],{"className":8302,"style":133},[74],[28,8304,192],{"className":8305},[79],[28,8307,195],{"className":8308},[79,80],[28,8310,54],{"className":8311},[85],[28,8313],{"className":8314,"style":90},[89],[28,8316,200],{"className":8317},[79,80],[28,8319],{"className":8320,"style":140},[89],[28,8322,203],{"className":8323},[144],[28,8325],{"className":8326,"style":140},[89],[28,8328,8330,8333],{"className":8329},[70],[28,8331],{"className":8332,"style":154},[74],[28,8334,49],{"className":8335,"style":81},[79,80],",\n",[28,8338,8340,8426],{"className":8339},[31],[28,8341,8343],{"className":8342},[35],[37,8344,8345],{"xmlns":39},[41,8346,8347,8423],{},[44,8348,8349,8351,8353,8355,8357,8359,8361,8363,8365,8367,8369,8371,8373,8375,8377,8379,8381,8383,8385,8387,8389,8391,8393,8395,8397,8399,8401,8403,8405,8407,8409,8411,8413,8415,8417,8419,8421],{},[47,8350,7688],{},[51,8352,269],{"stretchy":268},[47,8354,195],{},[51,8356,274],{},[47,8358,200],{},[51,8360,279],{"stretchy":268},[51,8362,282],{},[51,8364,269],{"stretchy":268},[47,8366,195],{},[51,8368,274],{},[47,8370,200],{},[51,8372,279],{"stretchy":268},[51,8374,274],{},[47,8376,7634],{},[51,8378,282],{},[51,8380,269],{"stretchy":268},[47,8382,195],{},[51,8384,274],{},[47,8386,7634],{},[51,8388,279],{"stretchy":268},[51,8390,274],{},[51,8392,269],{"stretchy":268},[47,8394,200],{},[51,8396,274],{},[47,8398,7634],{},[51,8400,279],{"stretchy":268},[51,8402,282],{},[47,8404,7688],{},[51,8406,269],{"stretchy":268},[47,8408,195],{},[51,8410,279],{"stretchy":268},[51,8412,274],{},[47,8414,7688],{},[51,8416,269],{"stretchy":268},[47,8418,200],{},[51,8420,279],{"stretchy":268},[47,8422,336],{"mathvariant":191},[59,8424,8425],{"encoding":61},"\\pi(a+b) = (a+b) + I = (a+I) + (b+I) = \\pi(a) + \\pi(b).",[28,8427,8429,8453,8474,8495,8516,8534,8555,8576,8597,8618,8645],{"className":8428,"ariaHidden":53},[66],[28,8430,8432,8435,8438,8441,8444,8447,8450],{"className":8431},[70],[28,8433],{"className":8434,"style":349},[74],[28,8436,7688],{"className":8437,"style":4471},[79,80],[28,8439,269],{"className":8440},[356],[28,8442,195],{"className":8443},[79,80],[28,8445],{"className":8446,"style":363},[89],[28,8448,274],{"className":8449},[367],[28,8451],{"className":8452,"style":363},[89],[28,8454,8456,8459,8462,8465,8468,8471],{"className":8455},[70],[28,8457],{"className":8458,"style":349},[74],[28,8460,200],{"className":8461},[79,80],[28,8463,279],{"className":8464},[383],[28,8466],{"className":8467,"style":140},[89],[28,8469,282],{"className":8470},[144],[28,8472],{"className":8473,"style":140},[89],[28,8475,8477,8480,8483,8486,8489,8492],{"className":8476},[70],[28,8478],{"className":8479,"style":349},[74],[28,8481,269],{"className":8482},[356],[28,8484,195],{"className":8485},[79,80],[28,8487],{"className":8488,"style":363},[89],[28,8490,274],{"className":8491},[367],[28,8493],{"className":8494,"style":363},[89],[28,8496,8498,8501,8504,8507,8510,8513],{"className":8497},[70],[28,8499],{"className":8500,"style":349},[74],[28,8502,200],{"className":8503},[79,80],[28,8505,279],{"className":8506},[383],[28,8508],{"className":8509,"style":363},[89],[28,8511,274],{"className":8512},[367],[28,8514],{"className":8515,"style":363},[89],[28,8517,8519,8522,8525,8528,8531],{"className":8518},[70],[28,8520],{"className":8521,"style":154},[74],[28,8523,7634],{"className":8524,"style":7654},[79,80],[28,8526],{"className":8527,"style":140},[89],[28,8529,282],{"className":8530},[144],[28,8532],{"className":8533,"style":140},[89],[28,8535,8537,8540,8543,8546,8549,8552],{"className":8536},[70],[28,8538],{"className":8539,"style":349},[74],[28,8541,269],{"className":8542},[356],[28,8544,195],{"className":8545},[79,80],[28,8547],{"className":8548,"style":363},[89],[28,8550,274],{"className":8551},[367],[28,8553],{"className":8554,"style":363},[89],[28,8556,8558,8561,8564,8567,8570,8573],{"className":8557},[70],[28,8559],{"className":8560,"style":349},[74],[28,8562,7634],{"className":8563,"style":7654},[79,80],[28,8565,279],{"className":8566},[383],[28,8568],{"className":8569,"style":363},[89],[28,8571,274],{"className":8572},[367],[28,8574],{"className":8575,"style":363},[89],[28,8577,8579,8582,8585,8588,8591,8594],{"className":8578},[70],[28,8580],{"className":8581,"style":349},[74],[28,8583,269],{"className":8584},[356],[28,8586,200],{"className":8587},[79,80],[28,8589],{"className":8590,"style":363},[89],[28,8592,274],{"className":8593},[367],[28,8595],{"className":8596,"style":363},[89],[28,8598,8600,8603,8606,8609,8612,8615],{"className":8599},[70],[28,8601],{"className":8602,"style":349},[74],[28,8604,7634],{"className":8605,"style":7654},[79,80],[28,8607,279],{"className":8608},[383],[28,8610],{"className":8611,"style":140},[89],[28,8613,282],{"className":8614},[144],[28,8616],{"className":8617,"style":140},[89],[28,8619,8621,8624,8627,8630,8633,8636,8639,8642],{"className":8620},[70],[28,8622],{"className":8623,"style":349},[74],[28,8625,7688],{"className":8626,"style":4471},[79,80],[28,8628,269],{"className":8629},[356],[28,8631,195],{"className":8632},[79,80],[28,8634,279],{"className":8635},[383],[28,8637],{"className":8638,"style":363},[89],[28,8640,274],{"className":8641},[367],[28,8643],{"className":8644,"style":363},[89],[28,8646,8648,8651,8654,8657,8660,8663],{"className":8647},[70],[28,8649],{"className":8650,"style":349},[74],[28,8652,7688],{"className":8653,"style":4471},[79,80],[28,8655,269],{"className":8656},[356],[28,8658,200],{"className":8659},[79,80],[28,8661,279],{"className":8662},[383],[28,8664,336],{"className":8665},[79],[545,8667,8668,1686,8671,8336,8739,8984,8985,9013,9014,9042,9043],{},[23,8669,8670],{},"保持乘法",[28,8672,8674,8697],{"className":8673},[31],[28,8675,8677],{"className":8676},[35],[37,8678,8679],{"xmlns":39},[41,8680,8681,8695],{},[44,8682,8683,8685,8687,8689,8691,8693],{},[47,8684,192],{"mathvariant":191},[47,8686,195],{},[51,8688,54],{"separator":53},[47,8690,200],{},[51,8692,203],{},[47,8694,49],{},[59,8696,208],{"encoding":61},[28,8698,8700,8730],{"className":8699,"ariaHidden":53},[66],[28,8701,8703,8706,8709,8712,8715,8718,8721,8724,8727],{"className":8702},[70],[28,8704],{"className":8705,"style":133},[74],[28,8707,192],{"className":8708},[79],[28,8710,195],{"className":8711},[79,80],[28,8713,54],{"className":8714},[85],[28,8716],{"className":8717,"style":90},[89],[28,8719,200],{"className":8720},[79,80],[28,8722],{"className":8723,"style":140},[89],[28,8725,203],{"className":8726},[144],[28,8728],{"className":8729,"style":140},[89],[28,8731,8733,8736],{"className":8732},[70],[28,8734],{"className":8735,"style":154},[74],[28,8737,49],{"className":8738,"style":81},[79,80],[28,8740,8742,8816],{"className":8741},[31],[28,8743,8745],{"className":8744},[35],[37,8746,8747],{"xmlns":39},[41,8748,8749,8813],{},[44,8750,8751,8753,8755,8757,8759,8761,8763,8765,8767,8769,8771,8773,8775,8777,8779,8781,8783,8785,8787,8789,8791,8793,8795,8797,8799,8801,8803,8805,8807,8809,8811],{},[47,8752,7688],{},[51,8754,269],{"stretchy":268},[47,8756,195],{},[47,8758,200],{},[51,8760,279],{"stretchy":268},[51,8762,282],{},[47,8764,195],{},[47,8766,200],{},[51,8768,274],{},[47,8770,7634],{},[51,8772,282],{},[51,8774,269],{"stretchy":268},[47,8776,195],{},[51,8778,274],{},[47,8780,7634],{},[51,8782,279],{"stretchy":268},[51,8784,269],{"stretchy":268},[47,8786,200],{},[51,8788,274],{},[47,8790,7634],{},[51,8792,279],{"stretchy":268},[51,8794,282],{},[47,8796,7688],{},[51,8798,269],{"stretchy":268},[47,8800,195],{},[51,8802,279],{"stretchy":268},[47,8804,7688],{},[51,8806,269],{"stretchy":268},[47,8808,200],{},[51,8810,279],{"stretchy":268},[47,8812,336],{"mathvariant":191},[59,8814,8815],{"encoding":61},"\\pi(ab) = ab + I = (a+I)(b+I) = \\pi(a)\\pi(b).",[28,8817,8819,8846,8864,8882,8903,8930,8951],{"className":8818,"ariaHidden":53},[66],[28,8820,8822,8825,8828,8831,8834,8837,8840,8843],{"className":8821},[70],[28,8823],{"className":8824,"style":349},[74],[28,8826,7688],{"className":8827,"style":4471},[79,80],[28,8829,269],{"className":8830},[356],[28,8832,457],{"className":8833},[79,80],[28,8835,279],{"className":8836},[383],[28,8838],{"className":8839,"style":140},[89],[28,8841,282],{"className":8842},[144],[28,8844],{"className":8845,"style":140},[89],[28,8847,8849,8852,8855,8858,8861],{"className":8848},[70],[28,8850],{"className":8851,"style":8239},[74],[28,8853,457],{"className":8854},[79,80],[28,8856],{"className":8857,"style":363},[89],[28,8859,274],{"className":8860},[367],[28,8862],{"className":8863,"style":363},[89],[28,8865,8867,8870,8873,8876,8879],{"className":8866},[70],[28,8868],{"className":8869,"style":154},[74],[28,8871,7634],{"className":8872,"style":7654},[79,80],[28,8874],{"className":8875,"style":140},[89],[28,8877,282],{"className":8878},[144],[28,8880],{"className":8881,"style":140},[89],[28,8883,8885,8888,8891,8894,8897,8900],{"className":8884},[70],[28,8886],{"className":8887,"style":349},[74],[28,8889,269],{"className":8890},[356],[28,8892,195],{"className":8893},[79,80],[28,8895],{"className":8896,"style":363},[89],[28,8898,274],{"className":8899},[367],[28,8901],{"className":8902,"style":363},[89],[28,8904,8906,8909,8912,8915,8918,8921,8924,8927],{"className":8905},[70],[28,8907],{"className":8908,"style":349},[74],[28,8910,7634],{"className":8911,"style":7654},[79,80],[28,8913,279],{"className":8914},[383],[28,8916,269],{"className":8917},[356],[28,8919,200],{"className":8920},[79,80],[28,8922],{"className":8923,"style":363},[89],[28,8925,274],{"className":8926},[367],[28,8928],{"className":8929,"style":363},[89],[28,8931,8933,8936,8939,8942,8945,8948],{"className":8932},[70],[28,8934],{"className":8935,"style":349},[74],[28,8937,7634],{"className":8938,"style":7654},[79,80],[28,8940,279],{"className":8941},[383],[28,8943],{"className":8944,"style":140},[89],[28,8946,282],{"className":8947},[144],[28,8949],{"className":8950,"style":140},[89],[28,8952,8954,8957,8960,8963,8966,8969,8972,8975,8978,8981],{"className":8953},[70],[28,8955],{"className":8956,"style":349},[74],[28,8958,7688],{"className":8959,"style":4471},[79,80],[28,8961,269],{"className":8962},[356],[28,8964,195],{"className":8965},[79,80],[28,8967,279],{"className":8968},[383],[28,8970,7688],{"className":8971,"style":4471},[79,80],[28,8973,269],{"className":8974},[356],[28,8976,200],{"className":8977},[79,80],[28,8979,279],{"className":8980},[383],[28,8982,336],{"className":8983},[79],"\n显见 ",[28,8986,8988,9001],{"className":8987},[31],[28,8989,8991],{"className":8990},[35],[37,8992,8993],{"xmlns":39},[41,8994,8995,8999],{},[44,8996,8997],{},[47,8998,7688],{},[59,9000,7870],{"encoding":61},[28,9002,9004],{"className":9003,"ariaHidden":53},[66],[28,9005,9007,9010],{"className":9006},[70],[28,9008],{"className":9009,"style":761},[74],[28,9011,7688],{"className":9012,"style":4471},[79,80]," 是满射。故 ",[28,9015,9017,9030],{"className":9016},[31],[28,9018,9020],{"className":9019},[35],[37,9021,9022],{"xmlns":39},[41,9023,9024,9028],{},[44,9025,9026],{},[47,9027,7688],{},[59,9029,7870],{"encoding":61},[28,9031,9033],{"className":9032,"ariaHidden":53},[66],[28,9034,9036,9039],{"className":9035},[70],[28,9037],{"className":9038,"style":761},[74],[28,9040,7688],{"className":9041,"style":4471},[79,80]," 是一个满的环同态。 ",[28,9044,9046,9059],{"className":9045},[31],[28,9047,9049],{"className":9048},[35],[37,9050,9051],{"xmlns":39},[41,9052,9053,9057],{},[44,9054,9055],{},[47,9056,6532],{"mathvariant":191},[59,9058,6535],{"encoding":61},[28,9060,9062],{"className":9061,"ariaHidden":53},[66],[28,9063,9065,9068],{"className":9064},[70],[28,9066],{"className":9067,"style":6545},[74],[28,9069,6532],{"className":9070},[79,2120],[20,9072,9073,26,9076,9126,9127,9199,9200,9262,9263,9291,9292,9429,9430,9547,9548,9630],{},[23,9074,9075],{},"定理 3.3.2 (第零同态定理 \u002F 通用性质).",[28,9077,9079,9096],{"className":9078},[31],[28,9080,9082],{"className":9081},[35],[37,9083,9084],{"xmlns":39},[41,9085,9086,9094],{},[44,9087,9088,9090,9092],{},[47,9089,7634],{},[51,9091,2090],{},[47,9093,49],{},[59,9095,7641],{"encoding":61},[28,9097,9099,9117],{"className":9098,"ariaHidden":53},[66],[28,9100,9102,9105,9108,9111,9114],{"className":9101},[70],[28,9103],{"className":9104,"style":6659},[74],[28,9106,7634],{"className":9107,"style":7654},[79,80],[28,9109],{"className":9110,"style":363},[89],[28,9112,2090],{"className":9113},[367,2120],[28,9115],{"className":9116,"style":363},[89],[28,9118,9120,9123],{"className":9119},[70],[28,9121],{"className":9122,"style":154},[74],[28,9124,49],{"className":9125,"style":81},[79,80],", 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是环同态，且 ",[28,9201,9203,9225],{"className":9202},[31],[28,9204,9206],{"className":9205},[35],[37,9207,9208],{"xmlns":39},[41,9209,9210,9222],{},[44,9211,9212,9214,9216,9218,9220],{},[47,9213,7634],{},[51,9215,2183],{},[47,9217,1701],{},[51,9219,1363],{},[47,9221,110],{},[59,9223,9224],{"encoding":61},"I \\le \\ker \\phi",[28,9226,9228,9247],{"className":9227,"ariaHidden":53},[66],[28,9229,9231,9235,9238,9241,9244],{"className":9230},[70],[28,9232],{"className":9233,"style":9234},[74],"height:0.8193em;vertical-align:-0.136em;",[28,9236,7634],{"className":9237,"style":7654},[79,80],[28,9239],{"className":9240,"style":140},[89],[28,9242,2183],{"className":9243},[144],[28,9245],{"className":9246,"style":140},[89],[28,9248,9250,9253,9256,9259],{"className":9249},[70],[28,9251],{"className":9252,"style":133},[74],[28,9254,1701],{"className":9255},[1385],[28,9257],{"className":9258,"style":90},[89],[28,9260,110],{"className":9261},[79,80],"（即 ",[28,9264,9266,9279],{"className":9265},[31],[28,9267,9269],{"className":9268},[35],[37,9270,9271],{"xmlns":39},[41,9272,9273,9277],{},[44,9274,9275],{},[47,9276,7634],{},[59,9278,7634],{"encoding":61},[28,9280,9282],{"className":9281,"ariaHidden":53},[66],[28,9283,9285,9288],{"className":9284},[70],[28,9286],{"className":9287,"style":154},[74],[28,9289,7634],{"className":9290,"style":7654},[79,80]," 包含在核内）。则存在唯一的环同态 ",[28,9293,9295,9327],{"className":9294},[31],[28,9296,9298],{"className":9297},[35],[37,9299,9300],{"xmlns":39},[41,9301,9302,9324],{},[44,9303,9304,9312,9314,9316,9318,9320,9322],{},[9305,9306,9307,9309],"mover",{"accent":53},[47,9308,110],{},[51,9310,9311],{},"ˉ",[51,9313,113],{},[47,9315,49],{},[47,9317,7699],{"mathvariant":191},[47,9319,7634],{},[51,9321,118],{},[47,9323,57],{},[59,9325,9326],{"encoding":61},"\\bar{\\phi}: R\u002FI \\to S",[28,9328,9330,9396,9420],{"className":9329,"ariaHidden":53},[66],[28,9331,9333,9337,9387,9390,9393],{"className":9332},[70],[28,9334],{"className":9335,"style":9336},[74],"height:1.0257em;vertical-align:-0.1944em;",[28,9338,9341],{"className":9339},[79,9340],"accent",[28,9342,9344,9378],{"className":9343},[2668,2669],[28,9345,9347,9375],{"className":9346},[2673],[28,9348,9351,9361],{"className":9349,"style":9350},[2677],"height:0.8312em;",[28,9352,9354,9358],{"style":9353},"top:-3em;",[28,9355],{"className":9356,"style":9357},[2685],"height:3em;",[28,9359,110],{"className":9360},[79,80],[28,9362,9364,9367],{"style":9363},"top:-3.2634em;",[28,9365],{"className":9366,"style":9357},[2685],[28,9368,9372],{"className":9369,"style":9371},[9370],"accent-body","left:-0.1667em;",[28,9373,9311],{"className":9374},[79],[28,9376,2701],{"className":9377},[2700],[28,9379,9381],{"className":9380},[2673],[28,9382,9385],{"className":9383,"style":9384},[2677],"height:0.1944em;",[28,9386],{},[28,9388],{"className":9389,"style":140},[89],[28,9391,113],{"className":9392},[144],[28,9394],{"className":9395,"style":140},[89],[28,9397,9399,9402,9405,9408,9411,9414,9417],{"className":9398},[70],[28,9400],{"className":9401,"style":349},[74],[28,9403,49],{"className":9404,"style":81},[79,80],[28,9406,7699],{"className":9407},[79],[28,9409,7634],{"className":9410,"style":7654},[79,80],[28,9412],{"className":9413,"style":140},[89],[28,9415,118],{"className":9416},[144],[28,9418],{"className":9419,"style":140},[89],[28,9421,9423,9426],{"className":9422},[70],[28,9424],{"className":9425,"style":154},[74],[28,9427,57],{"className":9428,"style":94},[79,80],", 满足 ",[28,9431,9433,9460],{"className":9432},[31],[28,9434,9436],{"className":9435},[35],[37,9437,9438],{"xmlns":39},[41,9439,9440,9457],{},[44,9441,9442,9444,9446,9452,9455],{},[47,9443,110],{},[51,9445,282],{},[9305,9447,9448,9450],{"accent":53},[47,9449,110],{},[51,9451,9311],{},[51,9453,9454],{},"∘",[47,9456,7688],{},[59,9458,9459],{"encoding":61},"\\phi = \\bar{\\phi} \\circ \\pi",[28,9461,9463,9481,9538],{"className":9462,"ariaHidden":53},[66],[28,9464,9466,9469,9472,9475,9478],{"className":9465},[70],[28,9467],{"className":9468,"style":133},[74],[28,9470,110],{"className":9471},[79,80],[28,9473],{"className":9474,"style":140},[89],[28,9476,282],{"className":9477},[144],[28,9479],{"className":9480,"style":140},[89],[28,9482,9484,9487,9529,9532,9535],{"className":9483},[70],[28,9485],{"className":9486,"style":9336},[74],[28,9488,9490],{"className":9489},[79,9340],[28,9491,9493,9521],{"className":9492},[2668,2669],[28,9494,9496,9518],{"className":9495},[2673],[28,9497,9499,9507],{"className":9498,"style":9350},[2677],[28,9500,9501,9504],{"style":9353},[28,9502],{"className":9503,"style":9357},[2685],[28,9505,110],{"className":9506},[79,80],[28,9508,9509,9512],{"style":9363},[28,9510],{"className":9511,"style":9357},[2685],[28,9513,9515],{"className":9514,"style":9371},[9370],[28,9516,9311],{"className":9517},[79],[28,9519,2701],{"className":9520},[2700],[28,9522,9524],{"className":9523},[2673],[28,9525,9527],{"className":9526,"style":9384},[2677],[28,9528],{},[28,9530],{"className":9531,"style":363},[89],[28,9533,9454],{"className":9534},[367],[28,9536],{"className":9537,"style":363},[89],[28,9539,9541,9544],{"className":9540},[70],[28,9542],{"className":9543,"style":761},[74],[28,9545,7688],{"className":9546,"style":4471},[79,80],", 其中 ",[28,9549,9551,9576],{"className":9550},[31],[28,9552,9554],{"className":9553},[35],[37,9555,9556],{"xmlns":39},[41,9557,9558,9574],{},[44,9559,9560,9562,9564,9566,9568,9570,9572],{},[47,9561,7688],{},[51,9563,113],{},[47,9565,49],{},[51,9567,118],{},[47,9569,49],{},[47,9571,7699],{"mathvariant":191},[47,9573,7634],{},[59,9575,7704],{"encoding":61},[28,9577,9579,9597,9615],{"className":9578,"ariaHidden":53},[66],[28,9580,9582,9585,9588,9591,9594],{"className":9581},[70],[28,9583],{"className":9584,"style":761},[74],[28,9586,7688],{"className":9587,"style":4471},[79,80],[28,9589],{"className":9590,"style":140},[89],[28,9592,113],{"className":9593},[144],[28,9595],{"className":9596,"style":140},[89],[28,9598,9600,9603,9606,9609,9612],{"className":9599},[70],[28,9601],{"className":9602,"style":154},[74],[28,9604,49],{"className":9605,"style":81},[79,80],[28,9607],{"className":9608,"style":140},[89],[28,9610,118],{"className":9611},[144],[28,9613],{"className":9614,"style":140},[89],[28,9616,9618,9621,9624,9627],{"className":9617},[70],[28,9619],{"className":9620,"style":349},[74],[28,9622,49],{"className":9623,"style":81},[79,80],[28,9625,7699],{"className":9626},[79],[28,9628,7634],{"className":9629,"style":7654},[79,80]," 是典范同态。",[20,9632,9633,26,9636,9708,9709,6907,9796],{},[23,9634,9635],{},"定理 3.3.3 (第一同态定理).",[28,9637,9639,9660],{"className":9638},[31],[28,9640,9642],{"className":9641},[35],[37,9643,9644],{"xmlns":39},[41,9645,9646,9658],{},[44,9647,9648,9650,9652,9654,9656],{},[47,9649,110],{},[51,9651,113],{},[47,9653,49],{},[51,9655,118],{},[47,9657,57],{},[59,9659,123],{"encoding":61},[28,9661,9663,9681,9699],{"className":9662,"ariaHidden":53},[66],[28,9664,9666,9669,9672,9675,9678],{"className":9665},[70],[28,9667],{"className":9668,"style":133},[74],[28,9670,110],{"className":9671},[79,80],[28,9673],{"className":9674,"style":140},[89],[28,9676,113],{"className":9677},[144],[28,9679],{"className":9680,"style":140},[89],[28,9682,9684,9687,9690,9693,9696],{"className":9683},[70],[28,9685],{"className":9686,"style":154},[74],[28,9688,49],{"className":9689,"style":81},[79,80],[28,9691],{"className":9692,"style":140},[89],[28,9694,118],{"className":9695},[144],[28,9697],{"className":9698,"style":140},[89],[28,9700,9702,9705],{"className":9701},[70],[28,9703],{"className":9704,"style":154},[74],[28,9706,57],{"className":9707,"style":94},[79,80]," 是环同态。则 ",[28,9710,9712,9742],{"className":9711},[31],[28,9713,9715],{"className":9714},[35],[37,9716,9717],{"xmlns":39},[41,9718,9719,9739],{},[44,9720,9721,9723,9725,9727,9729,9731,9733,9735,9737],{},[47,9722,49],{},[47,9724,7699],{"mathvariant":191},[47,9726,1701],{},[51,9728,1363],{},[47,9730,110],{},[51,9732,1166],{},[47,9734,1864],{"mathvariant":191},[51,9736,1363],{},[47,9738,110],{},[59,9740,9741],{"encoding":61},"R\u002F\\ker \\phi \\cong \\operatorname{Im} \\phi",[28,9743,9745,9778],{"className":9744,"ariaHidden":53},[66],[28,9746,9748,9751,9754,9757,9760,9763,9766,9769,9772,9775],{"className":9747},[70],[28,9749],{"className":9750,"style":349},[74],[28,9752,49],{"className":9753,"style":81},[79,80],[28,9755,7699],{"className":9756},[79],[28,9758],{"className":9759,"style":90},[89],[28,9761,1701],{"className":9762},[1385],[28,9764],{"className":9765,"style":90},[89],[28,9767,110],{"className":9768},[79,80],[28,9770],{"className":9771,"style":140},[89],[28,9773,1166],{"className":9774},[144],[28,9776],{"className":9777,"style":140},[89],[28,9779,9781,9784,9790,9793],{"className":9780},[70],[28,9782],{"className":9783,"style":133},[74],[28,9785,9787],{"className":9786},[1385],[28,9788,1864],{"className":9789},[79,1389],[28,9791],{"className":9792,"style":90},[89],[28,9794,110],{"className":9795},[79,80],[9797,9798,9799],"em",{},"(注：这是环论中最核心的定理，它建立了同态像与商环之间的代数同构关系。)",[20,9801,9802,9805,9806,9879,9880,9966,9967,10039,10040,10114,10115,1432,10143,10171],{},[23,9803,9804],{},"推论 3.3.1.","\n(i) 如果 ",[28,9807,9809,9831],{"className":9808},[31],[28,9810,9812],{"className":9811},[35],[37,9813,9814],{"xmlns":39},[41,9815,9816,9828],{},[44,9817,9818,9820,9822,9824,9826],{},[47,9819,110],{},[51,9821,113],{},[47,9823,49],{},[51,9825,118],{},[47,9827,49],{},[59,9829,9830],{"encoding":61},"\\phi: R \\to R",[28,9832,9834,9852,9870],{"className":9833,"ariaHidden":53},[66],[28,9835,9837,9840,9843,9846,9849],{"className":9836},[70],[28,9838],{"className":9839,"style":133},[74],[28,9841,110],{"className":9842},[79,80],[28,9844],{"className":9845,"style":140},[89],[28,9847,113],{"className":9848},[144],[28,9850],{"className":9851,"style":140},[89],[28,9853,9855,9858,9861,9864,9867],{"className":9854},[70],[28,9856],{"className":9857,"style":154},[74],[28,9859,49],{"className":9860,"style":81},[79,80],[28,9862],{"className":9863,"style":140},[89],[28,9865,118],{"className":9866},[144],[28,9868],{"className":9869,"style":140},[89],[28,9871,9873,9876],{"className":9872},[70],[28,9874],{"className":9875,"style":154},[74],[28,9877,49],{"className":9878,"style":81},[79,80]," 是单的环同态。则 ",[28,9881,9883,9909],{"className":9882},[31],[28,9884,9886],{"className":9885},[35],[37,9887,9888],{"xmlns":39},[41,9889,9890,9906],{},[44,9891,9892,9894,9896,9898,9900,9902,9904],{},[47,9893,49],{},[51,9895,1166],{},[47,9897,1864],{"mathvariant":191},[51,9899,1363],{},[47,9901,110],{},[51,9903,2183],{},[47,9905,57],{},[59,9907,9908],{"encoding":61},"R \\cong \\operatorname{Im} \\phi \\le S",[28,9910,9912,9930,9957],{"className":9911,"ariaHidden":53},[66],[28,9913,9915,9918,9921,9924,9927],{"className":9914},[70],[28,9916],{"className":9917,"style":154},[74],[28,9919,49],{"className":9920,"style":81},[79,80],[28,9922],{"className":9923,"style":140},[89],[28,9925,1166],{"className":9926},[144],[28,9928],{"className":9929,"style":140},[89],[28,9931,9933,9936,9942,9945,9948,9951,9954],{"className":9932},[70],[28,9934],{"className":9935,"style":133},[74],[28,9937,9939],{"className":9938},[1385],[28,9940,1864],{"className":9941},[79,1389],[28,9943],{"className":9944,"style":90},[89],[28,9946,110],{"className":9947},[79,80],[28,9949],{"className":9950,"style":140},[89],[28,9952,2183],{"className":9953},[144],[28,9955],{"className":9956,"style":140},[89],[28,9958,9960,9963],{"className":9959},[70],[28,9961],{"className":9962,"style":154},[74],[28,9964,57],{"className":9965,"style":94},[79,80],".\n(ii) 设 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是满的环同态。则 ",[28,10041,10043,10069],{"className":10042},[31],[28,10044,10046],{"className":10045},[35],[37,10047,10048],{"xmlns":39},[41,10049,10050,10066],{},[44,10051,10052,10054,10056,10058,10060,10062,10064],{},[47,10053,49],{},[47,10055,7699],{"mathvariant":191},[47,10057,1701],{},[51,10059,1363],{},[47,10061,110],{},[51,10063,1166],{},[47,10065,57],{},[59,10067,10068],{"encoding":61},"R\u002F\\ker \\phi \\cong S",[28,10070,10072,10105],{"className":10071,"ariaHidden":53},[66],[28,10073,10075,10078,10081,10084,10087,10090,10093,10096,10099,10102],{"className":10074},[70],[28,10076],{"className":10077,"style":349},[74],[28,10079,49],{"className":10080,"style":81},[79,80],[28,10082,7699],{"className":10083},[79],[28,10085],{"className":10086,"style":90},[89],[28,10088,1701],{"className":10089},[1385],[28,10091],{"className":10092,"style":90},[89],[28,10094,110],{"className":10095},[79,80],[28,10097],{"className":10098,"style":140},[89],[28,10100,1166],{"className":10101},[144],[28,10103],{"className":10104,"style":140},[89],[28,10106,10108,10111],{"className":10107},[70],[28,10109],{"className":10110,"style":154},[74],[28,10112,57],{"className":10113,"style":94},[79,80],", 称 ",[28,10116,10118,10131],{"className":10117},[31],[28,10119,10121],{"className":10120},[35],[37,10122,10123],{"xmlns":39},[41,10124,10125,10129],{},[44,10126,10127],{},[47,10128,57],{},[59,10130,57],{"encoding":61},[28,10132,10134],{"className":10133,"ariaHidden":53},[66],[28,10135,10137,10140],{"className":10136},[70],[28,10138],{"className":10139,"style":154},[74],[28,10141,57],{"className":10142,"style":94},[79,80],[28,10144,10146,10159],{"className":10145},[31],[28,10147,10149],{"className":10148},[35],[37,10150,10151],{"xmlns":39},[41,10152,10153,10157],{},[44,10154,10155],{},[47,10156,49],{},[59,10158,49],{"encoding":61},[28,10160,10162],{"className":10161,"ariaHidden":53},[66],[28,10163,10165,10168],{"className":10164},[70],[28,10166],{"className":10167,"style":154},[74],[28,10169,49],{"className":10170,"style":81},[79,80]," 的一个同态像。",[20,10173,10174,26,10177,6682,10227,10265,10266,10294,10295,10323,10324,10397,10398,336],{},[23,10175,10176],{},"定理 3.3.4 (第二同态定理 \u002F 对应定理).",[28,10178,10180,10197],{"className":10179},[31],[28,10181,10183],{"className":10182},[35],[37,10184,10185],{"xmlns":39},[41,10186,10187,10195],{},[44,10188,10189,10191,10193],{},[47,10190,7634],{},[51,10192,2090],{},[47,10194,49],{},[59,10196,7641],{"encoding":61},[28,10198,10200,10218],{"className":10199,"ariaHidden":53},[66],[28,10201,10203,10206,10209,10212,10215],{"className":10202},[70],[28,10204],{"className":10205,"style":6659},[74],[28,10207,7634],{"className":10208,"style":7654},[79,80],[28,10210],{"className":10211,"style":363},[89],[28,10213,2090],{"className":10214},[367,2120],[28,10216],{"className":10217,"style":363},[89],[28,10219,10221,10224],{"className":10220},[70],[28,10222],{"className":10223,"style":154},[74],[28,10225,49],{"className":10226,"style":81},[79,80],[28,10228,10230,10247],{"className":10229},[31],[28,10231,10233],{"className":10232},[35],[37,10234,10235],{"xmlns":39},[41,10236,10237,10245],{},[44,10238,10239,10241,10243],{},[47,10240,49],{},[47,10242,7699],{"mathvariant":191},[47,10244,7634],{},[59,10246,7904],{"encoding":61},[28,10248,10250],{"className":10249,"ariaHidden":53},[66],[28,10251,10253,10256,10259,10262],{"className":10252},[70],[28,10254],{"className":10255,"style":349},[74],[28,10257,49],{"className":10258,"style":81},[79,80],[28,10260,7699],{"className":10261},[79],[28,10263,7634],{"className":10264,"style":7654},[79,80]," 的子环(理想)与 ",[28,10267,10269,10282],{"className":10268},[31],[28,10270,10272],{"className":10271},[35],[37,10273,10274],{"xmlns":39},[41,10275,10276,10280],{},[44,10277,10278],{},[47,10279,49],{},[59,10281,49],{"encoding":61},[28,10283,10285],{"className":10284,"ariaHidden":53},[66],[28,10286,10288,10291],{"className":10287},[70],[28,10289],{"className":10290,"style":154},[74],[28,10292,49],{"className":10293,"style":81},[79,80]," 的包含 ",[28,10296,10298,10311],{"className":10297},[31],[28,10299,10301],{"className":10300},[35],[37,10302,10303],{"xmlns":39},[41,10304,10305,10309],{},[44,10306,10307],{},[47,10308,7634],{},[59,10310,7634],{"encoding":61},[28,10312,10314],{"className":10313,"ariaHidden":53},[66],[28,10315,10317,10320],{"className":10316},[70],[28,10318],{"className":10319,"style":154},[74],[28,10321,7634],{"className":10322,"style":7654},[79,80]," 的子环(理想)一一对应。如果 ",[28,10325,10327,10349],{"className":10326},[31],[28,10328,10330],{"className":10329},[35],[37,10331,10332],{"xmlns":39},[41,10333,10334,10346],{},[44,10335,10336,10338,10340,10342,10344],{},[47,10337,7634],{},[51,10339,2090],{},[47,10341,6642],{},[51,10343,2090],{},[47,10345,49],{},[59,10347,10348],{"encoding":61},"I \\lhd J \\lhd R",[28,10350,10352,10370,10388],{"className":10351,"ariaHidden":53},[66],[28,10353,10355,10358,10361,10364,10367],{"className":10354},[70],[28,10356],{"className":10357,"style":6659},[74],[28,10359,7634],{"className":10360,"style":7654},[79,80],[28,10362],{"className":10363,"style":363},[89],[28,10365,2090],{"className":10366},[367,2120],[28,10368],{"className":10369,"style":363},[89],[28,10371,10373,10376,10379,10382,10385],{"className":10372},[70],[28,10374],{"className":10375,"style":6659},[74],[28,10377,6642],{"className":10378,"style":6663},[79,80],[28,10380],{"className":10381,"style":363},[89],[28,10383,2090],{"className":10384},[367,2120],[28,10386],{"className":10387,"style":363},[89],[28,10389,10391,10394],{"className":10390},[70],[28,10392],{"className":10393,"style":154},[74],[28,10395,49],{"className":10396,"style":81},[79,80],", 则有 ",[28,10399,10401,10443],{"className":10400},[31],[28,10402,10404],{"className":10403},[35],[37,10405,10406],{"xmlns":39},[41,10407,10408,10440],{},[44,10409,10410,10412,10414,10416,10418,10420,10422,10424,10426,10428,10430,10432,10434,10436,10438],{},[47,10411,49],{},[47,10413,7699],{"mathvariant":191},[47,10415,6642],{},[51,10417,1166],{},[51,10419,269],{"stretchy":268},[47,10421,49],{},[47,10423,7699],{"mathvariant":191},[47,10425,7634],{},[51,10427,279],{"stretchy":268},[47,10429,7699],{"mathvariant":191},[51,10431,269],{"stretchy":268},[47,10433,6642],{},[47,10435,7699],{"mathvariant":191},[47,10437,7634],{},[51,10439,279],{"stretchy":268},[59,10441,10442],{"encoding":61},"R\u002FJ \\cong (R\u002FI)\u002F(J\u002FI)",[28,10444,10446,10470],{"className":10445,"ariaHidden":53},[66],[28,10447,10449,10452,10455,10458,10461,10464,10467],{"className":10448},[70],[28,10450],{"className":10451,"style":349},[74],[28,10453,49],{"className":10454,"style":81},[79,80],[28,10456,7699],{"className":10457},[79],[28,10459,6642],{"className":10460,"style":6663},[79,80],[28,10462],{"className":10463,"style":140},[89],[28,10465,1166],{"className":10466},[144],[28,10468],{"className":10469,"style":140},[89],[28,10471,10473,10476,10479,10482,10485,10488,10491,10494,10497,10500,10503,10506],{"className":10472},[70],[28,10474],{"className":10475,"style":349},[74],[28,10477,269],{"className":10478},[356],[28,10480,49],{"className":10481,"style":81},[79,80],[28,10483,7699],{"className":10484},[79],[28,10486,7634],{"className":10487,"style":7654},[79,80],[28,10489,279],{"className":10490},[383],[28,10492,7699],{"className":10493},[79],[28,10495,269],{"className":10496},[356],[28,10498,6642],{"className":10499,"style":6663},[79,80],[28,10501,7699],{"className":10502},[79],[28,10504,7634],{"className":10505,"style":7654},[79,80],[28,10507,279],{"className":10508},[383],[20,10510,10511,26,10514,6682,10602,10734,10735],{},[23,10512,10513],{},"定理 3.3.5 (第三同态定理).",[28,10515,10517,10544],{"className":10516},[31],[28,10518,10520],{"className":10519},[35],[37,10521,10522],{"xmlns":39},[41,10523,10524,10541],{},[44,10525,10526,10528,10530,10532,10534,10537,10539],{},[47,10527,7634],{},[51,10529,2090],{},[47,10531,49],{},[51,10533,54],{"separator":53},[47,10535,10536],{},"K",[51,10538,2183],{},[47,10540,49],{},[59,10542,10543],{"encoding":61},"I \\lhd R, K \\le R",[28,10545,10547,10565,10593],{"className":10546,"ariaHidden":53},[66],[28,10548,10550,10553,10556,10559,10562],{"className":10549},[70],[28,10551],{"className":10552,"style":6659},[74],[28,10554,7634],{"className":10555,"style":7654},[79,80],[28,10557],{"className":10558,"style":363},[89],[28,10560,2090],{"className":10561},[367,2120],[28,10563],{"className":10564,"style":363},[89],[28,10566,10568,10571,10574,10577,10580,10584,10587,10590],{"className":10567},[70],[28,10569],{"className":10570,"style":75},[74],[28,10572,49],{"className":10573,"style":81},[79,80],[28,10575,54],{"className":10576},[85],[28,10578],{"className":10579,"style":90},[89],[28,10581,10536],{"className":10582,"style":10583},[79,80],"margin-right:0.0715em;",[28,10585],{"className":10586,"style":140},[89],[28,10588,2183],{"className":10589},[144],[28,10591],{"className":10592,"style":140},[89],[28,10594,10596,10599],{"className":10595},[70],[28,10597],{"className":10598,"style":154},[74],[28,10600,49],{"className":10601,"style":81},[79,80],[28,10603,10605,10640],{"className":10604},[31],[28,10606,10608],{"className":10607},[35],[37,10609,10610],{"xmlns":39},[41,10611,10612,10637],{},[44,10613,10614,10616,10618,10620,10622,10624,10626,10628,10631,10633,10635],{},[47,10615,7634],{},[51,10617,274],{},[47,10619,10536],{},[51,10621,2183],{},[47,10623,49],{},[51,10625,54],{"separator":53},[47,10627,7634],{},[51,10629,10630],{},"∩",[47,10632,10536],{},[51,10634,2090],{},[47,10636,10536],{},[59,10638,10639],{"encoding":61},"I+K \\le R, I \\cap K \\lhd K",[28,10641,10643,10662,10680,10707,10725],{"className":10642,"ariaHidden":53},[66],[28,10644,10646,10650,10653,10656,10659],{"className":10645},[70],[28,10647],{"className":10648,"style":10649},[74],"height:0.7667em;vertical-align:-0.0833em;",[28,10651,7634],{"className":10652,"style":7654},[79,80],[28,10654],{"className":10655,"style":363},[89],[28,10657,274],{"className":10658},[367],[28,10660],{"className":10661,"style":363},[89],[28,10663,10665,10668,10671,10674,10677],{"className":10664},[70],[28,10666],{"className":10667,"style":9234},[74],[28,10669,10536],{"className":10670,"style":10583},[79,80],[28,10672],{"className":10673,"style":140},[89],[28,10675,2183],{"className":10676},[144],[28,10678],{"className":10679,"style":140},[89],[28,10681,10683,10686,10689,10692,10695,10698,10701,10704],{"className":10682},[70],[28,10684],{"className":10685,"style":75},[74],[28,10687,49],{"className":10688,"style":81},[79,80],[28,10690,54],{"className":10691},[85],[28,10693],{"className":10694,"style":90},[89],[28,10696,7634],{"className":10697,"style":7654},[79,80],[28,10699],{"className":10700,"style":363},[89],[28,10702,10630],{"className":10703},[367],[28,10705],{"className":10706,"style":363},[89],[28,10708,10710,10713,10716,10719,10722],{"className":10709},[70],[28,10711],{"className":10712,"style":6659},[74],[28,10714,10536],{"className":10715,"style":10583},[79,80],[28,10717],{"className":10718,"style":363},[89],[28,10720,2090],{"className":10721},[367,2120],[28,10723],{"className":10724,"style":363},[89],[28,10726,10728,10731],{"className":10727},[70],[28,10729],{"className":10730,"style":154},[74],[28,10732,10536],{"className":10733,"style":10583},[79,80],", 且\n",[28,10736,10738,10782],{"className":10737},[31],[28,10739,10741],{"className":10740},[35],[37,10742,10743],{"xmlns":39},[41,10744,10745,10779],{},[44,10746,10747,10749,10751,10753,10755,10757,10759,10761,10763,10765,10767,10769,10771,10773,10775,10777],{},[51,10748,269],{"stretchy":268},[47,10750,7634],{},[51,10752,274],{},[47,10754,10536],{},[51,10756,279],{"stretchy":268},[47,10758,7699],{"mathvariant":191},[47,10760,7634],{},[51,10762,1166],{},[47,10764,10536],{},[47,10766,7699],{"mathvariant":191},[51,10768,269],{"stretchy":268},[47,10770,7634],{},[51,10772,10630],{},[47,10774,10536],{},[51,10776,279],{"stretchy":268},[47,10778,336],{"mathvariant":191},[59,10780,10781],{"encoding":61},"(I+K)\u002FI \\cong K\u002F(I \\cap K).",[28,10783,10785,10806,10833,10860],{"className":10784,"ariaHidden":53},[66],[28,10786,10788,10791,10794,10797,10800,10803],{"className":10787},[70],[28,10789],{"className":10790,"style":349},[74],[28,10792,269],{"className":10793},[356],[28,10795,7634],{"className":10796,"style":7654},[79,80],[28,10798],{"className":10799,"style":363},[89],[28,10801,274],{"className":10802},[367],[28,10804],{"className":10805,"style":363},[89],[28,10807,10809,10812,10815,10818,10821,10824,10827,10830],{"className":10808},[70],[28,10810],{"className":10811,"style":349},[74],[28,10813,10536],{"className":10814,"style":10583},[79,80],[28,10816,279],{"className":10817},[383],[28,10819,7699],{"className":10820},[79],[28,10822,7634],{"className":10823,"style":7654},[79,80],[28,10825],{"className":10826,"style":140},[89],[28,10828,1166],{"className":10829},[144],[28,10831],{"className":10832,"style":140},[89],[28,10834,10836,10839,10842,10845,10848,10851,10854,10857],{"className":10835},[70],[28,10837],{"className":10838,"style":349},[74],[28,10840,10536],{"className":10841,"style":10583},[79,80],[28,10843,7699],{"className":10844},[79],[28,10846,269],{"className":10847},[356],[28,10849,7634],{"className":10850,"style":7654},[79,80],[28,10852],{"className":10853,"style":363},[89],[28,10855,10630],{"className":10856},[367],[28,10858],{"className":10859,"style":363},[89],[28,10861,10863,10866,10869,10872],{"className":10862},[70],[28,10864],{"className":10865,"style":349},[74],[28,10867,10536],{"className":10868,"style":10583},[79,80],[28,10870,279],{"className":10871},[383],[28,10873,336],{"className":10874},[79],[20,10876,10877,10879,10880,1461,10908,10979],{},[23,10878,2362],{},"\n此定理描述了子环与理想之和的商结构。证明思路是构造一个从 ",[28,10881,10883,10896],{"className":10882},[31],[28,10884,10886],{"className":10885},[35],[37,10887,10888],{"xmlns":39},[41,10889,10890,10894],{},[44,10891,10892],{},[47,10893,10536],{},[59,10895,10536],{"encoding":61},[28,10897,10899],{"className":10898,"ariaHidden":53},[66],[28,10900,10902,10905],{"className":10901},[70],[28,10903],{"className":10904,"style":154},[74],[28,10906,10536],{"className":10907,"style":10583},[79,80],[28,10909,10911,10937],{"className":10910},[31],[28,10912,10914],{"className":10913},[35],[37,10915,10916],{"xmlns":39},[41,10917,10918,10934],{},[44,10919,10920,10922,10924,10926,10928,10930,10932],{},[51,10921,269],{"stretchy":268},[47,10923,7634],{},[51,10925,274],{},[47,10927,10536],{},[51,10929,279],{"stretchy":268},[47,10931,7699],{"mathvariant":191},[47,10933,7634],{},[59,10935,10936],{"encoding":61},"(I+K)\u002FI",[28,10938,10940,10961],{"className":10939,"ariaHidden":53},[66],[28,10941,10943,10946,10949,10952,10955,10958],{"className":10942},[70],[28,10944],{"className":10945,"style":349},[74],[28,10947,269],{"className":10948},[356],[28,10950,7634],{"className":10951,"style":7654},[79,80],[28,10953],{"className":10954,"style":363},[89],[28,10956,274],{"className":10957},[367],[28,10959],{"className":10960,"style":363},[89],[28,10962,10964,10967,10970,10973,10976],{"className":10963},[70],[28,10965],{"className":10966,"style":349},[74],[28,10968,10536],{"className":10969,"style":10583},[79,80],[28,10971,279],{"className":10972},[383],[28,10974,7699],{"className":10975},[79],[28,10977,7634],{"className":10978,"style":7654},[79,80]," 的满同态，并利用第一同态定理。",[542,10981,10982,11415,12846,13425,14085],{},[545,10983,10984,10987,10988,11104,11105,11195,11196,2770,11292,11343,11344,11414],{},[23,10985,10986],{},"构造映射",": 定义 ",[28,10989,10991,11026],{"className":10990},[31],[28,10992,10994],{"className":10993},[35],[37,10995,10996],{"xmlns":39},[41,10997,10998,11023],{},[44,10999,11000,11003,11005,11007,11009,11011,11013,11015,11017,11019,11021],{},[47,11001,11002],{},"ψ",[51,11004,113],{},[47,11006,10536],{},[51,11008,118],{},[51,11010,269],{"stretchy":268},[47,11012,7634],{},[51,11014,274],{},[47,11016,10536],{},[51,11018,279],{"stretchy":268},[47,11020,7699],{"mathvariant":191},[47,11022,7634],{},[59,11024,11025],{"encoding":61},"\\psi: K \\to (I+K)\u002FI",[28,11027,11029,11047,11065,11086],{"className":11028,"ariaHidden":53},[66],[28,11030,11032,11035,11038,11041,11044],{"className":11031},[70],[28,11033],{"className":11034,"style":133},[74],[28,11036,11002],{"className":11037,"style":4471},[79,80],[28,11039],{"className":11040,"style":140},[89],[28,11042,113],{"className":11043},[144],[28,11045],{"className":11046,"style":140},[89],[28,11048,11050,11053,11056,11059,11062],{"className":11049},[70],[28,11051],{"className":11052,"style":154},[74],[28,11054,10536],{"className":11055,"style":10583},[79,80],[28,11057],{"className":11058,"style":140},[89],[28,11060,118],{"className":11061},[144],[28,11063],{"className":11064,"style":140},[89],[28,11066,11068,11071,11074,11077,11080,11083],{"className":11067},[70],[28,11069],{"className":11070,"style":349},[74],[28,11072,269],{"className":11073},[356],[28,11075,7634],{"className":11076,"style":7654},[79,80],[28,11078],{"className":11079,"style":363},[89],[28,11081,274],{"className":11082},[367],[28,11084],{"className":11085,"style":363},[89],[28,11087,11089,11092,11095,11098,11101],{"className":11088},[70],[28,11090],{"className":11091,"style":349},[74],[28,11093,10536],{"className":11094,"style":10583},[79,80],[28,11096,279],{"className":11097},[383],[28,11099,7699],{"className":11100},[79],[28,11102,7634],{"className":11103,"style":7654},[79,80],"，规则为 ",[28,11106,11108,11137],{"className":11107},[31],[28,11109,11111],{"className":11110},[35],[37,11112,11113],{"xmlns":39},[41,11114,11115,11134],{},[44,11116,11117,11119,11121,11124,11126,11128,11130,11132],{},[47,11118,11002],{},[51,11120,269],{"stretchy":268},[47,11122,11123],{},"k",[51,11125,279],{"stretchy":268},[51,11127,282],{},[47,11129,11123],{},[51,11131,274],{},[47,11133,7634],{},[59,11135,11136],{"encoding":61},"\\psi(k) = k + I",[28,11138,11140,11168,11186],{"className":11139,"ariaHidden":53},[66],[28,11141,11143,11146,11149,11152,11156,11159,11162,11165],{"className":11142},[70],[28,11144],{"className":11145,"style":349},[74],[28,11147,11002],{"className":11148,"style":4471},[79,80],[28,11150,269],{"className":11151},[356],[28,11153,11123],{"className":11154,"style":11155},[79,80],"margin-right:0.0315em;",[28,11157,279],{"className":11158},[383],[28,11160],{"className":11161,"style":140},[89],[28,11163,282],{"className":11164},[144],[28,11166],{"className":11167,"style":140},[89],[28,11169,11171,11174,11177,11180,11183],{"className":11170},[70],[28,11172],{"className":11173,"style":8239},[74],[28,11175,11123],{"className":11176,"style":11155},[79,80],[28,11178],{"className":11179,"style":363},[89],[28,11181,274],{"className":11182},[367],[28,11184],{"className":11185,"style":363},[89],[28,11187,11189,11192],{"className":11188},[70],[28,11190],{"className":11191,"style":154},[74],[28,11193,7634],{"className":11194,"style":7654},[79,80],"。\n注意：这里 ",[28,11197,11199,11226],{"className":11198},[31],[28,11200,11202],{"className":11201},[35],[37,11203,11204],{"xmlns":39},[41,11205,11206,11223],{},[44,11207,11208,11210,11212,11214,11217,11219,11221],{},[47,11209,11123],{},[51,11211,203],{},[47,11213,10536],{},[51,11215,11216],{},"⊆",[47,11218,7634],{},[51,11220,274],{},[47,11222,10536],{},[59,11224,11225],{"encoding":61},"k \\in K \\subseteq I+K",[28,11227,11229,11247,11265,11283],{"className":11228,"ariaHidden":53},[66],[28,11230,11232,11235,11238,11241,11244],{"className":11231},[70],[28,11233],{"className":11234,"style":893},[74],[28,11236,11123],{"className":11237,"style":11155},[79,80],[28,11239],{"className":11240,"style":140},[89],[28,11242,203],{"className":11243},[144],[28,11245],{"className":11246,"style":140},[89],[28,11248,11250,11253,11256,11259,11262],{"className":11249},[70],[28,11251],{"className":11252,"style":9234},[74],[28,11254,10536],{"className":11255,"style":10583},[79,80],[28,11257],{"className":11258,"style":140},[89],[28,11260,11216],{"className":11261},[144],[28,11263],{"className":11264,"style":140},[89],[28,11266,11268,11271,11274,11277,11280],{"className":11267},[70],[28,11269],{"className":11270,"style":10649},[74],[28,11272,7634],{"className":11273,"style":7654},[79,80],[28,11275],{"className":11276,"style":363},[89],[28,11278,274],{"className":11279},[367],[28,11281],{"className":11282,"style":363},[89],[28,11284,11286,11289],{"className":11285},[70],[28,11287],{"className":11288,"style":154},[74],[28,11290,10536],{"className":11291,"style":10583},[79,80],[28,11293,11295,11313],{"className":11294},[31],[28,11296,11298],{"className":11297},[35],[37,11299,11300],{"xmlns":39},[41,11301,11302,11310],{},[44,11303,11304,11306,11308],{},[47,11305,11123],{},[51,11307,274],{},[47,11309,7634],{},[59,11311,11312],{"encoding":61},"k+I",[28,11314,11316,11334],{"className":11315,"ariaHidden":53},[66],[28,11317,11319,11322,11325,11328,11331],{"className":11318},[70],[28,11320],{"className":11321,"style":8239},[74],[28,11323,11123],{"className":11324,"style":11155},[79,80],[28,11326],{"className":11327,"style":363},[89],[28,11329,274],{"className":11330},[367],[28,11332],{"className":11333,"style":363},[89],[28,11335,11337,11340],{"className":11336},[70],[28,11338],{"className":11339,"style":154},[74],[28,11341,7634],{"className":11342,"style":7654},[79,80]," 确实是商环 ",[28,11345,11347,11372],{"className":11346},[31],[28,11348,11350],{"className":11349},[35],[37,11351,11352],{"xmlns":39},[41,11353,11354,11370],{},[44,11355,11356,11358,11360,11362,11364,11366,11368],{},[51,11357,269],{"stretchy":268},[47,11359,7634],{},[51,11361,274],{},[47,11363,10536],{},[51,11365,279],{"stretchy":268},[47,11367,7699],{"mathvariant":191},[47,11369,7634],{},[59,11371,10936],{"encoding":61},[28,11373,11375,11396],{"className":11374,"ariaHidden":53},[66],[28,11376,11378,11381,11384,11387,11390,11393],{"className":11377},[70],[28,11379],{"className":11380,"style":349},[74],[28,11382,269],{"className":11383},[356],[28,11385,7634],{"className":11386,"style":7654},[79,80],[28,11388],{"className":11389,"style":363},[89],[28,11391,274],{"className":11392},[367],[28,11394],{"className":11395,"style":363},[89],[28,11397,11399,11402,11405,11408,11411],{"className":11398},[70],[28,11400],{"className":11401,"style":349},[74],[28,11403,10536],{"className":11404,"style":10583},[79,80],[28,11406,279],{"className":11407},[383],[28,11409,7699],{"className":11410},[79],[28,11412,7634],{"className":11413,"style":7654},[79,80]," 中的元素。",[545,11416,11417,1686,11420,8336,11574],{},[23,11418,11419],{},"验证同态",[28,11421,11423,11456],{"className":11422},[31],[28,11424,11426],{"className":11425},[35],[37,11427,11428],{"xmlns":39},[41,11429,11430,11453],{},[44,11431,11432,11434,11440,11442,11449,11451],{},[47,11433,192],{"mathvariant":191},[2621,11435,11436,11438],{},[47,11437,11123],{},[1731,11439,6706],{},[51,11441,54],{"separator":53},[2621,11443,11444,11446],{},[47,11445,11123],{},[1731,11447,11448],{},"2",[51,11450,203],{},[47,11452,10536],{},[59,11454,11455],{"encoding":61},"\\forall k_1, k_2 \\in K",[28,11457,11459,11565],{"className":11458,"ariaHidden":53},[66],[28,11460,11462,11465,11468,11510,11513,11516,11556,11559,11562],{"className":11461},[70],[28,11463],{"className":11464,"style":133},[74],[28,11466,192],{"className":11467},[79],[28,11469,11471,11474],{"className":11470},[79],[28,11472,11123],{"className":11473,"style":11155},[79,80],[28,11475,11477],{"className":11476},[2664],[28,11478,11480,11502],{"className":11479},[2668,2669],[28,11481,11483,11499],{"className":11482},[2673],[28,11484,11487],{"className":11485,"style":11486},[2677],"height:0.3011em;",[28,11488,11490,11493],{"style":11489},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[28,11491],{"className":11492,"style":2686},[2685],[28,11494,11496],{"className":11495},[2690,2691,2692,2693],[28,11497,6706],{"className":11498},[79,2693],[28,11500,2701],{"className":11501},[2700],[28,11503,11505],{"className":11504},[2673],[28,11506,11508],{"className":11507,"style":2708},[2677],[28,11509],{},[28,11511,54],{"className":11512},[85],[28,11514],{"className":11515,"style":90},[89],[28,11517,11519,11522],{"className":11518},[79],[28,11520,11123],{"className":11521,"style":11155},[79,80],[28,11523,11525],{"className":11524},[2664],[28,11526,11528,11548],{"className":11527},[2668,2669],[28,11529,11531,11545],{"className":11530},[2673],[28,11532,11534],{"className":11533,"style":11486},[2677],[28,11535,11536,11539],{"style":11489},[28,11537],{"className":11538,"style":2686},[2685],[28,11540,11542],{"className":11541},[2690,2691,2692,2693],[28,11543,11448],{"className":11544},[79,2693],[28,11546,2701],{"className":11547},[2700],[28,11549,11551],{"className":11550},[2673],[28,11552,11554],{"className":11553,"style":2708},[2677],[28,11555],{},[28,11557],{"className":11558,"style":140},[89],[28,11560,203],{"className":11561},[144],[28,11563],{"className":11564,"style":140},[89],[28,11566,11568,11571],{"className":11567},[70],[28,11569],{"className":11570,"style":154},[74],[28,11572,10536],{"className":11573,"style":10583},[79,80],[1679,11575,11576,12230],{},[545,11577,11578,336],{},[28,11579,11581,11697],{"className":11580},[31],[28,11582,11584],{"className":11583},[35],[37,11585,11586],{"xmlns":39},[41,11587,11588,11694],{},[44,11589,11590,11592,11594,11600,11602,11608,11610,11612,11614,11620,11622,11628,11630,11632,11634,11636,11638,11644,11646,11648,11650,11652,11654,11660,11662,11664,11666,11668,11670,11672,11678,11680,11682,11684,11686,11692],{},[47,11591,11002],{},[51,11593,269],{"stretchy":268},[2621,11595,11596,11598],{},[47,11597,11123],{},[1731,11599,6706],{},[51,11601,274],{},[2621,11603,11604,11606],{},[47,11605,11123],{},[1731,11607,11448],{},[51,11609,279],{"stretchy":268},[51,11611,282],{},[51,11613,269],{"stretchy":268},[2621,11615,11616,11618],{},[47,11617,11123],{},[1731,11619,6706],{},[51,11621,274],{},[2621,11623,11624,11626],{},[47,11625,11123],{},[1731,11627,11448],{},[51,11629,279],{"stretchy":268},[51,11631,274],{},[47,11633,7634],{},[51,11635,282],{},[51,11637,269],{"stretchy":268},[2621,11639,11640,11642],{},[47,11641,11123],{},[1731,11643,6706],{},[51,11645,274],{},[47,11647,7634],{},[51,11649,279],{"stretchy":268},[51,11651,274],{},[51,11653,269],{"stretchy":268},[2621,11655,11656,11658],{},[47,11657,11123],{},[1731,11659,11448],{},[51,11661,274],{},[47,11663,7634],{},[51,11665,279],{"stretchy":268},[51,11667,282],{},[47,11669,11002],{},[51,11671,269],{"stretchy":268},[2621,11673,11674,11676],{},[47,11675,11123],{},[1731,11677,6706],{},[51,11679,279],{"stretchy":268},[51,11681,274],{},[47,11683,11002],{},[51,11685,269],{"stretchy":268},[2621,11687,11688,11690],{},[47,11689,11123],{},[1731,11691,11448],{},[51,11693,279],{"stretchy":268},[59,11695,11696],{"encoding":61},"\\psi(k_1+k_2) = (k_1+k_2)+I = (k_1+I)+(k_2+I) = \\psi(k_1)+\\psi(k_2)",[28,11698,11700,11761,11819,11877,11935,11953,12011,12032,12090,12111,12175],{"className":11699,"ariaHidden":53},[66],[28,11701,11703,11706,11709,11712,11752,11755,11758],{"className":11702},[70],[28,11704],{"className":11705,"style":349},[74],[28,11707,11002],{"className":11708,"style":4471},[79,80],[28,11710,269],{"className":11711},[356],[28,11713,11715,11718],{"className":11714},[79],[28,11716,11123],{"className":11717,"style":11155},[79,80],[28,11719,11721],{"className":11720},[2664],[28,11722,11724,11744],{"className":11723},[2668,2669],[28,11725,11727,11741],{"className":11726},[2673],[28,11728,11730],{"className":11729,"style":11486},[2677],[28,11731,11732,11735],{"style":11489},[28,11733],{"className":11734,"style":2686},[2685],[28,11736,11738],{"className":11737},[2690,2691,2692,2693],[28,11739,6706],{"className":11740},[79,2693],[28,11742,2701],{"className":11743},[2700],[28,11745,11747],{"className":11746},[2673],[28,11748,11750],{"className":11749,"style":2708},[2677],[28,11751],{},[28,11753],{"className":11754,"style":363},[89],[28,11756,274],{"className":11757},[367],[28,11759],{"className":11760,"style":363},[89],[28,11762,11764,11767,11807,11810,11813,11816],{"className":11763},[70],[28,11765],{"className":11766,"style":349},[74],[28,11768,11770,11773],{"className":11769},[79],[28,11771,11123],{"className":11772,"style":11155},[79,80],[28,11774,11776],{"className":11775},[2664],[28,11777,11779,11799],{"className":11778},[2668,2669],[28,11780,11782,11796],{"className":11781},[2673],[28,11783,11785],{"className":11784,"style":11486},[2677],[28,11786,11787,11790],{"style":11489},[28,11788],{"className":11789,"style":2686},[2685],[28,11791,11793],{"className":11792},[2690,2691,2692,2693],[28,11794,11448],{"className":11795},[79,2693],[28,11797,2701],{"className":11798},[2700],[28,11800,11802],{"className":11801},[2673],[28,11803,11805],{"className":11804,"style":2708},[2677],[28,11806],{},[28,11808,279],{"className":11809},[383],[28,11811],{"className":11812,"style":140},[89],[28,11814,282],{"className":11815},[144],[28,11817],{"className":11818,"style":140},[89],[28,11820,11822,11825,11828,11868,11871,11874],{"className":11821},[70],[28,11823],{"className":11824,"style":349},[74],[28,11826,269],{"className":11827},[356],[28,11829,11831,11834],{"className":11830},[79],[28,11832,11123],{"className":11833,"style":11155},[79,80],[28,11835,11837],{"className":11836},[2664],[28,11838,11840,11860],{"className":11839},[2668,2669],[28,11841,11843,11857],{"className":11842},[2673],[28,11844,11846],{"className":11845,"style":11486},[2677],[28,11847,11848,11851],{"style":11489},[28,11849],{"className":11850,"style":2686},[2685],[28,11852,11854],{"className":11853},[2690,2691,2692,2693],[28,11855,6706],{"className":11856},[79,2693],[28,11858,2701],{"className":11859},[2700],[28,11861,11863],{"className":11862},[2673],[28,11864,11866],{"className":11865,"style":2708},[2677],[28,11867],{},[28,11869],{"className":11870,"style":363},[89],[28,11872,274],{"className":11873},[367],[28,11875],{"className":11876,"style":363},[89],[28,11878,11880,11883,11923,11926,11929,11932],{"className":11879},[70],[28,11881],{"className":11882,"style":349},[74],[28,11884,11886,11889],{"className":11885},[79],[28,11887,11123],{"className":11888,"style":11155},[79,80],[28,11890,11892],{"className":11891},[2664],[28,11893,11895,11915],{"className":11894},[2668,2669],[28,11896,11898,11912],{"className":11897},[2673],[28,11899,11901],{"className":11900,"style":11486},[2677],[28,11902,11903,11906],{"style":11489},[28,11904],{"className":11905,"style":2686},[2685],[28,11907,11909],{"className":11908},[2690,2691,2692,2693],[28,11910,11448],{"className":11911},[79,2693],[28,11913,2701],{"className":11914},[2700],[28,11916,11918],{"className":11917},[2673],[28,11919,11921],{"className":11920,"style":2708},[2677],[28,11922],{},[28,11924,279],{"className":11925},[383],[28,11927],{"className":11928,"style":363},[89],[28,11930,274],{"className":11931},[367],[28,11933],{"className":11934,"style":363},[89],[28,11936,11938,11941,11944,11947,11950],{"className":11937},[70],[28,11939],{"className":11940,"style":154},[74],[28,11942,7634],{"className":11943,"style":7654},[79,80],[28,11945],{"className":11946,"style":140},[89],[28,11948,282],{"className":11949},[144],[28,11951],{"className":11952,"style":140},[89],[28,11954,11956,11959,11962,12002,12005,12008],{"className":11955},[70],[28,11957],{"className":11958,"style":349},[74],[28,11960,269],{"className":11961},[356],[28,11963,11965,11968],{"className":11964},[79],[28,11966,11123],{"className":11967,"style":11155},[79,80],[28,11969,11971],{"className":11970},[2664],[28,11972,11974,11994],{"className":11973},[2668,2669],[28,11975,11977,11991],{"className":11976},[2673],[28,11978,11980],{"className":11979,"style":11486},[2677],[28,11981,11982,11985],{"style":11489},[28,11983],{"className":11984,"style":2686},[2685],[28,11986,11988],{"className":11987},[2690,2691,2692,2693],[28,11989,6706],{"className":11990},[79,2693],[28,11992,2701],{"className":11993},[2700],[28,11995,11997],{"className":11996},[2673],[28,11998,12000],{"className":11999,"style":2708},[2677],[28,12001],{},[28,12003],{"className":12004,"style":363},[89],[28,12006,274],{"className":12007},[367],[28,12009],{"className":12010,"style":363},[89],[28,12012,12014,12017,12020,12023,12026,12029],{"className":12013},[70],[28,12015],{"className":12016,"style":349},[74],[28,12018,7634],{"className":12019,"style":7654},[79,80],[28,12021,279],{"className":12022},[383],[28,12024],{"className":12025,"style":363},[89],[28,12027,274],{"className":12028},[367],[28,12030],{"className":12031,"style":363},[89],[28,12033,12035,12038,12041,12081,12084,12087],{"className":12034},[70],[28,12036],{"className":12037,"style":349},[74],[28,12039,269],{"className":12040},[356],[28,12042,12044,12047],{"className":12043},[79],[28,12045,11123],{"className":12046,"style":11155},[79,80],[28,12048,12050],{"className":12049},[2664],[28,12051,12053,12073],{"className":12052},[2668,2669],[28,12054,12056,12070],{"className":12055},[2673],[28,12057,12059],{"className":12058,"style":11486},[2677],[28,12060,12061,12064],{"style":11489},[28,12062],{"className":12063,"style":2686},[2685],[28,12065,12067],{"className":12066},[2690,2691,2692,2693],[28,12068,11448],{"className":12069},[79,2693],[28,12071,2701],{"className":12072},[2700],[28,12074,12076],{"className":12075},[2673],[28,12077,12079],{"className":12078,"style":2708},[2677],[28,12080],{},[28,12082],{"className":12083,"style":363},[89],[28,12085,274],{"className":12086},[367],[28,12088],{"className":12089,"style":363},[89],[28,12091,12093,12096,12099,12102,12105,12108],{"className":12092},[70],[28,12094],{"className":12095,"style":349},[74],[28,12097,7634],{"className":12098,"style":7654},[79,80],[28,12100,279],{"className":12101},[383],[28,12103],{"className":12104,"style":140},[89],[28,12106,282],{"className":12107},[144],[28,12109],{"className":12110,"style":140},[89],[28,12112,12114,12117,12120,12123,12163,12166,12169,12172],{"className":12113},[70],[28,12115],{"className":12116,"style":349},[74],[28,12118,11002],{"className":12119,"style":4471},[79,80],[28,12121,269],{"className":12122},[356],[28,12124,12126,12129],{"className":12125},[79],[28,12127,11123],{"className":12128,"style":11155},[79,80],[28,12130,12132],{"className":12131},[2664],[28,12133,12135,12155],{"className":12134},[2668,2669],[28,12136,12138,12152],{"className":12137},[2673],[28,12139,12141],{"className":12140,"style":11486},[2677],[28,12142,12143,12146],{"style":11489},[28,12144],{"className":12145,"style":2686},[2685],[28,12147,12149],{"className":12148},[2690,2691,2692,2693],[28,12150,6706],{"className":12151},[79,2693],[28,12153,2701],{"className":12154},[2700],[28,12156,12158],{"className":12157},[2673],[28,12159,12161],{"className":12160,"style":2708},[2677],[28,12162],{},[28,12164,279],{"className":12165},[383],[28,12167],{"className":12168,"style":363},[89],[28,12170,274],{"className":12171},[367],[28,12173],{"className":12174,"style":363},[89],[28,12176,12178,12181,12184,12187,12227],{"className":12177},[70],[28,12179],{"className":12180,"style":349},[74],[28,12182,11002],{"className":12183,"style":4471},[79,80],[28,12185,269],{"className":12186},[356],[28,12188,12190,12193],{"className":12189},[79],[28,12191,11123],{"className":12192,"style":11155},[79,80],[28,12194,12196],{"className":12195},[2664],[28,12197,12199,12219],{"className":12198},[2668,2669],[28,12200,12202,12216],{"className":12201},[2673],[28,12203,12205],{"className":12204,"style":11486},[2677],[28,12206,12207,12210],{"style":11489},[28,12208],{"className":12209,"style":2686},[2685],[28,12211,12213],{"className":12212},[2690,2691,2692,2693],[28,12214,11448],{"className":12215},[79,2693],[28,12217,2701],{"className":12218},[2700],[28,12220,12222],{"className":12221},[2673],[28,12223,12225],{"className":12224,"style":2708},[2677],[28,12226],{},[28,12228,279],{"className":12229},[383],[545,12231,12232,12816,12817,1677],{},[28,12233,12235,12343],{"className":12234},[31],[28,12236,12238],{"className":12237},[35],[37,12239,12240],{"xmlns":39},[41,12241,12242,12340],{},[44,12243,12244,12246,12248,12254,12260,12262,12264,12266,12272,12278,12280,12282,12284,12286,12288,12294,12296,12298,12300,12302,12308,12310,12312,12314,12316,12318,12320,12326,12328,12330,12332,12338],{},[47,12245,11002],{},[51,12247,269],{"stretchy":268},[2621,12249,12250,12252],{},[47,12251,11123],{},[1731,12253,6706],{},[2621,12255,12256,12258],{},[47,12257,11123],{},[1731,12259,11448],{},[51,12261,279],{"stretchy":268},[51,12263,282],{},[51,12265,269],{"stretchy":268},[2621,12267,12268,12270],{},[47,12269,11123],{},[1731,12271,6706],{},[2621,12273,12274,12276],{},[47,12275,11123],{},[1731,12277,11448],{},[51,12279,279],{"stretchy":268},[51,12281,274],{},[47,12283,7634],{},[51,12285,282],{},[51,12287,269],{"stretchy":268},[2621,12289,12290,12292],{},[47,12291,11123],{},[1731,12293,6706],{},[51,12295,274],{},[47,12297,7634],{},[51,12299,279],{"stretchy":268},[51,12301,269],{"stretchy":268},[2621,12303,12304,12306],{},[47,12305,11123],{},[1731,12307,11448],{},[51,12309,274],{},[47,12311,7634],{},[51,12313,279],{"stretchy":268},[51,12315,282],{},[47,12317,11002],{},[51,12319,269],{"stretchy":268},[2621,12321,12322,12324],{},[47,12323,11123],{},[1731,12325,6706],{},[51,12327,279],{"stretchy":268},[47,12329,11002],{},[51,12331,269],{"stretchy":268},[2621,12333,12334,12336],{},[47,12335,11123],{},[1731,12337,11448],{},[51,12339,279],{"stretchy":268},[59,12341,12342],{"encoding":61},"\\psi(k_1 k_2) = (k_1 k_2)+I = (k_1+I)(k_2+I) = \\psi(k_1)\\psi(k_2)",[28,12344,12346,12450,12551,12569,12627,12691,12712],{"className":12345,"ariaHidden":53},[66],[28,12347,12349,12352,12355,12358,12398,12438,12441,12444,12447],{"className":12348},[70],[28,12350],{"className":12351,"style":349},[74],[28,12353,11002],{"className":12354,"style":4471},[79,80],[28,12356,269],{"className":12357},[356],[28,12359,12361,12364],{"className":12360},[79],[28,12362,11123],{"className":12363,"style":11155},[79,80],[28,12365,12367],{"className":12366},[2664],[28,12368,12370,12390],{"className":12369},[2668,2669],[28,12371,12373,12387],{"className":12372},[2673],[28,12374,12376],{"className":12375,"style":11486},[2677],[28,12377,12378,12381],{"style":11489},[28,12379],{"className":12380,"style":2686},[2685],[28,12382,12384],{"className":12383},[2690,2691,2692,2693],[28,12385,6706],{"className":12386},[79,2693],[28,12388,2701],{"className":12389},[2700],[28,12391,12393],{"className":12392},[2673],[28,12394,12396],{"className":12395,"style":2708},[2677],[28,12397],{},[28,12399,12401,12404],{"className":12400},[79],[28,12402,11123],{"className":12403,"style":11155},[79,80],[28,12405,12407],{"className":12406},[2664],[28,12408,12410,12430],{"className":12409},[2668,2669],[28,12411,12413,12427],{"className":12412},[2673],[28,12414,12416],{"className":12415,"style":11486},[2677],[28,12417,12418,12421],{"style":11489},[28,12419],{"className":12420,"style":2686},[2685],[28,12422,12424],{"className":12423},[2690,2691,2692,2693],[28,12425,11448],{"className":12426},[79,2693],[28,12428,2701],{"className":12429},[2700],[28,12431,12433],{"className":12432},[2673],[28,12434,12436],{"className":12435,"style":2708},[2677],[28,12437],{},[28,12439,279],{"className":12440},[383],[28,12442],{"className":12443,"style":140},[89],[28,12445,282],{"className":12446},[144],[28,12448],{"className":12449,"style":140},[89],[28,12451,12453,12456,12459,12499,12539,12542,12545,12548],{"className":12452},[70],[28,12454],{"className":12455,"style":349},[74],[28,12457,269],{"className":12458},[356],[28,12460,12462,12465],{"className":12461},[79],[28,12463,11123],{"className":12464,"style":11155},[79,80],[28,12466,12468],{"className":12467},[2664],[28,12469,12471,12491],{"className":12470},[2668,2669],[28,12472,12474,12488],{"className":12473},[2673],[28,12475,12477],{"className":12476,"style":11486},[2677],[28,12478,12479,12482],{"style":11489},[28,12480],{"className":12481,"style":2686},[2685],[28,12483,12485],{"className":12484},[2690,2691,2692,2693],[28,12486,6706],{"className":12487},[79,2693],[28,12489,2701],{"className":12490},[2700],[28,12492,12494],{"className":12493},[2673],[28,12495,12497],{"className":12496,"style":2708},[2677],[28,12498],{},[28,12500,12502,12505],{"className":12501},[79],[28,12503,11123],{"className":12504,"style":11155},[79,80],[28,12506,12508],{"className":12507},[2664],[28,12509,12511,12531],{"className":12510},[2668,2669],[28,12512,12514,12528],{"className":12513},[2673],[28,12515,12517],{"className":12516,"style":11486},[2677],[28,12518,12519,12522],{"style":11489},[28,12520],{"className":12521,"style":2686},[2685],[28,12523,12525],{"className":12524},[2690,2691,2692,2693],[28,12526,11448],{"className":12527},[79,2693],[28,12529,2701],{"className":12530},[2700],[28,12532,12534],{"className":12533},[2673],[28,12535,12537],{"className":12536,"style":2708},[2677],[28,12538],{},[28,12540,279],{"className":12541},[383],[28,12543],{"className":12544,"style":363},[89],[28,12546,274],{"className":12547},[367],[28,12549],{"className":12550,"style":363},[89],[28,12552,12554,12557,12560,12563,12566],{"className":12553},[70],[28,12555],{"className":12556,"style":154},[74],[28,12558,7634],{"className":12559,"style":7654},[79,80],[28,12561],{"className":12562,"style":140},[89],[28,12564,282],{"className":12565},[144],[28,12567],{"className":12568,"style":140},[89],[28,12570,12572,12575,12578,12618,12621,12624],{"className":12571},[70],[28,12573],{"className":12574,"style":349},[74],[28,12576,269],{"className":12577},[356],[28,12579,12581,12584],{"className":12580},[79],[28,12582,11123],{"className":12583,"style":11155},[79,80],[28,12585,12587],{"className":12586},[2664],[28,12588,12590,12610],{"className":12589},[2668,2669],[28,12591,12593,12607],{"className":12592},[2673],[28,12594,12596],{"className":12595,"style":11486},[2677],[28,12597,12598,12601],{"style":11489},[28,12599],{"className":12600,"style":2686},[2685],[28,12602,12604],{"className":12603},[2690,2691,2692,2693],[28,12605,6706],{"className":12606},[79,2693],[28,12608,2701],{"className":12609},[2700],[28,12611,12613],{"className":12612},[2673],[28,12614,12616],{"className":12615,"style":2708},[2677],[28,12617],{},[28,12619],{"className":12620,"style":363},[89],[28,12622,274],{"className":12623},[367],[28,12625],{"className":12626,"style":363},[89],[28,12628,12630,12633,12636,12639,12642,12682,12685,12688],{"className":12629},[70],[28,12631],{"className":12632,"style":349},[74],[28,12634,7634],{"className":12635,"style":7654},[79,80],[28,12637,279],{"className":12638},[383],[28,12640,269],{"className":12641},[356],[28,12643,12645,12648],{"className":12644},[79],[28,12646,11123],{"className":12647,"style":11155},[79,80],[28,12649,12651],{"className":12650},[2664],[28,12652,12654,12674],{"className":12653},[2668,2669],[28,12655,12657,12671],{"className":12656},[2673],[28,12658,12660],{"className":12659,"style":11486},[2677],[28,12661,12662,12665],{"style":11489},[28,12663],{"className":12664,"style":2686},[2685],[28,12666,12668],{"className":12667},[2690,2691,2692,2693],[28,12669,11448],{"className":12670},[79,2693],[28,12672,2701],{"className":12673},[2700],[28,12675,12677],{"className":12676},[2673],[28,12678,12680],{"className":12679,"style":2708},[2677],[28,12681],{},[28,12683],{"className":12684,"style":363},[89],[28,12686,274],{"className":12687},[367],[28,12689],{"className":12690,"style":363},[89],[28,12692,12694,12697,12700,12703,12706,12709],{"className":12693},[70],[28,12695],{"className":12696,"style":349},[74],[28,12698,7634],{"className":12699,"style":7654},[79,80],[28,12701,279],{"className":12702},[383],[28,12704],{"className":12705,"style":140},[89],[28,12707,282],{"className":12708},[144],[28,12710],{"className":12711,"style":140},[89],[28,12713,12715,12718,12721,12724,12764,12767,12770,12773,12813],{"className":12714},[70],[28,12716],{"className":12717,"style":349},[74],[28,12719,11002],{"className":12720,"style":4471},[79,80],[28,12722,269],{"className":12723},[356],[28,12725,12727,12730],{"className":12726},[79],[28,12728,11123],{"className":12729,"style":11155},[79,80],[28,12731,12733],{"className":12732},[2664],[28,12734,12736,12756],{"className":12735},[2668,2669],[28,12737,12739,12753],{"className":12738},[2673],[28,12740,12742],{"className":12741,"style":11486},[2677],[28,12743,12744,12747],{"style":11489},[28,12745],{"className":12746,"style":2686},[2685],[28,12748,12750],{"className":12749},[2690,2691,2692,2693],[28,12751,6706],{"className":12752},[79,2693],[28,12754,2701],{"className":12755},[2700],[28,12757,12759],{"className":12758},[2673],[28,12760,12762],{"className":12761,"style":2708},[2677],[28,12763],{},[28,12765,279],{"className":12766},[383],[28,12768,11002],{"className":12769,"style":4471},[79,80],[28,12771,269],{"className":12772},[356],[28,12774,12776,12779],{"className":12775},[79],[28,12777,11123],{"className":12778,"style":11155},[79,80],[28,12780,12782],{"className":12781},[2664],[28,12783,12785,12805],{"className":12784},[2668,2669],[28,12786,12788,12802],{"className":12787},[2673],[28,12789,12791],{"className":12790,"style":11486},[2677],[28,12792,12793,12796],{"style":11489},[28,12794],{"className":12795,"style":2686},[2685],[28,12797,12799],{"className":12798},[2690,2691,2692,2693],[28,12800,11448],{"className":12801},[79,2693],[28,12803,2701],{"className":12804},[2700],[28,12806,12808],{"className":12807},[2673],[28,12809,12811],{"className":12810,"style":2708},[2677],[28,12812],{},[28,12814,279],{"className":12815},[383],".\n所以 ",[28,12818,12820,12834],{"className":12819},[31],[28,12821,12823],{"className":12822},[35],[37,12824,12825],{"xmlns":39},[41,12826,12827,12831],{},[44,12828,12829],{},[47,12830,11002],{},[59,12832,12833],{"encoding":61},"\\psi",[28,12835,12837],{"className":12836,"ariaHidden":53},[66],[28,12838,12840,12843],{"className":12839},[70],[28,12841],{"className":12842,"style":133},[74],[28,12844,11002],{"className":12845,"style":4471},[79,80],[545,12847,12848,4910,12851,12921,12922,13006,13007,13094,13095,13298,13299,13350,13351,13395,13396,13424],{},[23,12849,12850],{},"验证满射",[28,12852,12854,12879],{"className":12853},[31],[28,12855,12857],{"className":12856},[35],[37,12858,12859],{"xmlns":39},[41,12860,12861,12877],{},[44,12862,12863,12865,12867,12869,12871,12873,12875],{},[51,12864,269],{"stretchy":268},[47,12866,7634],{},[51,12868,274],{},[47,12870,10536],{},[51,12872,279],{"stretchy":268},[47,12874,7699],{"mathvariant":191},[47,12876,7634],{},[59,12878,10936],{"encoding":61},[28,12880,12882,12903],{"className":12881,"ariaHidden":53},[66],[28,12883,12885,12888,12891,12894,12897,12900],{"className":12884},[70],[28,12886],{"className":12887,"style":349},[74],[28,12889,269],{"className":12890},[356],[28,12892,7634],{"className":12893,"style":7654},[79,80],[28,12895],{"className":12896,"style":363},[89],[28,12898,274],{"className":12899},[367],[28,12901],{"className":12902,"style":363},[89],[28,12904,12906,12909,12912,12915,12918],{"className":12905},[70],[28,12907],{"className":12908,"style":349},[74],[28,12910,10536],{"className":12911,"style":10583},[79,80],[28,12913,279],{"className":12914},[383],[28,12916,7699],{"className":12917},[79],[28,12919,7634],{"className":12920,"style":7654},[79,80]," 中的任意元素形式为 ",[28,12923,12925,12952],{"className":12924},[31],[28,12926,12928],{"className":12927},[35],[37,12929,12930],{"xmlns":39},[41,12931,12932,12949],{},[44,12933,12934,12936,12939,12941,12943,12945,12947],{},[51,12935,269],{"stretchy":268},[47,12937,12938],{},"i",[51,12940,274],{},[47,12942,11123],{},[51,12944,279],{"stretchy":268},[51,12946,274],{},[47,12948,7634],{},[59,12950,12951],{"encoding":61},"(i+k)+I",[28,12953,12955,12976,12997],{"className":12954,"ariaHidden":53},[66],[28,12956,12958,12961,12964,12967,12970,12973],{"className":12957},[70],[28,12959],{"className":12960,"style":349},[74],[28,12962,269],{"className":12963},[356],[28,12965,12938],{"className":12966},[79,80],[28,12968],{"className":12969,"style":363},[89],[28,12971,274],{"className":12972},[367],[28,12974],{"className":12975,"style":363},[89],[28,12977,12979,12982,12985,12988,12991,12994],{"className":12978},[70],[28,12980],{"className":12981,"style":349},[74],[28,12983,11123],{"className":12984,"style":11155},[79,80],[28,12986,279],{"className":12987},[383],[28,12989],{"className":12990,"style":363},[89],[28,12992,274],{"className":12993},[367],[28,12995],{"className":12996,"style":363},[89],[28,12998,13000,13003],{"className":12999},[70],[28,13001],{"className":13002,"style":154},[74],[28,13004,7634],{"className":13005,"style":7654},[79,80],"，其中 ",[28,13008,13010,13036],{"className":13009},[31],[28,13011,13013],{"className":13012},[35],[37,13014,13015],{"xmlns":39},[41,13016,13017,13033],{},[44,13018,13019,13021,13023,13025,13027,13029,13031],{},[47,13020,12938],{},[51,13022,203],{},[47,13024,7634],{},[51,13026,54],{"separator":53},[47,13028,11123],{},[51,13030,203],{},[47,13032,10536],{},[59,13034,13035],{"encoding":61},"i \\in I, k \\in K",[28,13037,13039,13058,13085],{"className":13038,"ariaHidden":53},[66],[28,13040,13042,13046,13049,13052,13055],{"className":13041},[70],[28,13043],{"className":13044,"style":13045},[74],"height:0.6986em;vertical-align:-0.0391em;",[28,13047,12938],{"className":13048},[79,80],[28,13050],{"className":13051,"style":140},[89],[28,13053,203],{"className":13054},[144],[28,13056],{"className":13057,"style":140},[89],[28,13059,13061,13064,13067,13070,13073,13076,13079,13082],{"className":13060},[70],[28,13062],{"className":13063,"style":133},[74],[28,13065,7634],{"className":13066,"style":7654},[79,80],[28,13068,54],{"className":13069},[85],[28,13071],{"className":13072,"style":90},[89],[28,13074,11123],{"className":13075,"style":11155},[79,80],[28,13077],{"className":13078,"style":140},[89],[28,13080,203],{"className":13081},[144],[28,13083],{"className":13084,"style":140},[89],[28,13086,13088,13091],{"className":13087},[70],[28,13089],{"className":13090,"style":154},[74],[28,13092,10536],{"className":13093,"style":10583},[79,80],"。\n根据商环陪集的性质，",[28,13096,13098,13148],{"className":13097},[31],[28,13099,13101],{"className":13100},[35],[37,13102,13103],{"xmlns":39},[41,13104,13105,13145],{},[44,13106,13107,13109,13111,13113,13115,13117,13119,13121,13123,13125,13127,13129,13131,13133,13135,13137,13139,13141,13143],{},[51,13108,269],{"stretchy":268},[47,13110,12938],{},[51,13112,274],{},[47,13114,11123],{},[51,13116,279],{"stretchy":268},[51,13118,274],{},[47,13120,7634],{},[51,13122,282],{},[47,13124,11123],{},[51,13126,274],{},[51,13128,269],{"stretchy":268},[47,13130,12938],{},[51,13132,274],{},[47,13134,7634],{},[51,13136,279],{"stretchy":268},[51,13138,282],{},[47,13140,11123],{},[51,13142,274],{},[47,13144,7634],{},[59,13146,13147],{"encoding":61},"(i+k)+I = k+(i+I) = k+I",[28,13149,13151,13172,13193,13211,13229,13250,13271,13289],{"className":13150,"ariaHidden":53},[66],[28,13152,13154,13157,13160,13163,13166,13169],{"className":13153},[70],[28,13155],{"className":13156,"style":349},[74],[28,13158,269],{"className":13159},[356],[28,13161,12938],{"className":13162},[79,80],[28,13164],{"className":13165,"style":363},[89],[28,13167,274],{"className":13168},[367],[28,13170],{"className":13171,"style":363},[89],[28,13173,13175,13178,13181,13184,13187,13190],{"className":13174},[70],[28,13176],{"className":13177,"style":349},[74],[28,13179,11123],{"className":13180,"style":11155},[79,80],[28,13182,279],{"className":13183},[383],[28,13185],{"className":13186,"style":363},[89],[28,13188,274],{"className":13189},[367],[28,13191],{"className":13192,"style":363},[89],[28,13194,13196,13199,13202,13205,13208],{"className":13195},[70],[28,13197],{"className":13198,"style":154},[74],[28,13200,7634],{"className":13201,"style":7654},[79,80],[28,13203],{"className":13204,"style":140},[89],[28,13206,282],{"className":13207},[144],[28,13209],{"className":13210,"style":140},[89],[28,13212,13214,13217,13220,13223,13226],{"className":13213},[70],[28,13215],{"className":13216,"style":8239},[74],[28,13218,11123],{"className":13219,"style":11155},[79,80],[28,13221],{"className":13222,"style":363},[89],[28,13224,274],{"className":13225},[367],[28,13227],{"className":13228,"style":363},[89],[28,13230,13232,13235,13238,13241,13244,13247],{"className":13231},[70],[28,13233],{"className":13234,"style":349},[74],[28,13236,269],{"className":13237},[356],[28,13239,12938],{"className":13240},[79,80],[28,13242],{"className":13243,"style":363},[89],[28,13245,274],{"className":13246},[367],[28,13248],{"className":13249,"style":363},[89],[28,13251,13253,13256,13259,13262,13265,13268],{"className":13252},[70],[28,13254],{"className":13255,"style":349},[74],[28,13257,7634],{"className":13258,"style":7654},[79,80],[28,13260,279],{"className":13261},[383],[28,13263],{"className":13264,"style":140},[89],[28,13266,282],{"className":13267},[144],[28,13269],{"className":13270,"style":140},[89],[28,13272,13274,13277,13280,13283,13286],{"className":13273},[70],[28,13275],{"className":13276,"style":8239},[74],[28,13278,11123],{"className":13279,"style":11155},[79,80],[28,13281],{"className":13282,"style":363},[89],[28,13284,274],{"className":13285},[367],[28,13287],{"className":13288,"style":363},[89],[28,13290,13292,13295],{"className":13291},[70],[28,13293],{"className":13294,"style":154},[74],[28,13296,7634],{"className":13297,"style":7654},[79,80],"（因为 ",[28,13300,13302,13320],{"className":13301},[31],[28,13303,13305],{"className":13304},[35],[37,13306,13307],{"xmlns":39},[41,13308,13309,13317],{},[44,13310,13311,13313,13315],{},[47,13312,12938],{},[51,13314,203],{},[47,13316,7634],{},[59,13318,13319],{"encoding":61},"i \\in I",[28,13321,13323,13341],{"className":13322,"ariaHidden":53},[66],[28,13324,13326,13329,13332,13335,13338],{"className":13325},[70],[28,13327],{"className":13328,"style":13045},[74],[28,13330,12938],{"className":13331},[79,80],[28,13333],{"className":13334,"style":140},[89],[28,13336,203],{"className":13337},[144],[28,13339],{"className":13340,"style":140},[89],[28,13342,13344,13347],{"className":13343},[70],[28,13345],{"className":13346,"style":154},[74],[28,13348,7634],{"className":13349,"style":7654},[79,80],"）。\n即任意元素均可写成 ",[28,13352,13354,13374],{"className":13353},[31],[28,13355,13357],{"className":13356},[35],[37,13358,13359],{"xmlns":39},[41,13360,13361,13371],{},[44,13362,13363,13365,13367,13369],{},[47,13364,11002],{},[51,13366,269],{"stretchy":268},[47,13368,11123],{},[51,13370,279],{"stretchy":268},[59,13372,13373],{"encoding":61},"\\psi(k)",[28,13375,13377],{"className":13376,"ariaHidden":53},[66],[28,13378,13380,13383,13386,13389,13392],{"className":13379},[70],[28,13381],{"className":13382,"style":349},[74],[28,13384,11002],{"className":13385,"style":4471},[79,80],[28,13387,269],{"className":13388},[356],[28,13390,11123],{"className":13391,"style":11155},[79,80],[28,13393,279],{"className":13394},[383]," 的形式，故 ",[28,13397,13399,13412],{"className":13398},[31],[28,13400,13402],{"className":13401},[35],[37,13403,13404],{"xmlns":39},[41,13405,13406,13410],{},[44,13407,13408],{},[47,13409,11002],{},[59,13411,12833],{"encoding":61},[28,13413,13415],{"className":13414,"ariaHidden":53},[66],[28,13416,13418,13421],{"className":13417},[70],[28,13419],{"className":13420,"style":133},[74],[28,13422,11002],{"className":13423,"style":4471},[79,80]," 是满同态。",[545,13426,13427,4910,13469],{},[23,13428,13429,13430,279],{},"计算核 (",[28,13431,13433,13451],{"className":13432},[31],[28,13434,13436],{"className":13435},[35],[37,13437,13438],{"xmlns":39},[41,13439,13440,13448],{},[44,13441,13442,13444,13446],{},[47,13443,1701],{},[51,13445,1363],{},[47,13447,11002],{},[59,13449,13450],{"encoding":61},"\\ker \\psi",[28,13452,13454],{"className":13453,"ariaHidden":53},[66],[28,13455,13457,13460,13463,13466],{"className":13456},[70],[28,13458],{"className":13459,"style":133},[74],[28,13461,1701],{"className":13462},[1385],[28,13464],{"className":13465,"style":90},[89],[28,13467,11002],{"className":13468,"style":4471},[79,80],[28,13470,13472,13659],{"className":13471},[31],[28,13473,13475],{"className":13474},[35],[37,13476,13477],{"xmlns":39},[41,13478,13479,13656],{},[13480,13481,13485,13554,13594,13630],"mtable",{"rowspacing":13482,"columnalign":13483,"columnspacing":13484},"0.25em","right 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\\ker \\psi &= \\{k \\in K \\mid \\psi(k) = 0_{(I+K)\u002FI}\\} \\\\ &= \\{k \\in K \\mid k+I = I\\} \\\\ &= \\{k \\in K \\mid k \\in I\\} \\\\ &= K \\cap I. \\end{aligned}",[28,13660,13662],{"className":13661,"ariaHidden":53},[66],[28,13663,13665,13669],{"className":13664},[70],[28,13666],{"className":13667,"style":13668},[74],"height:5.7em;vertical-align:-2.6em;",[28,13670,13672],{"className":13671},[79],[28,13673,13675,13746],{"className":13674},[13480],[28,13676,13679],{"className":13677},[13678],"col-align-r",[28,13680,13682,13737],{"className":13681},[2668,2669],[28,13683,13685,13734],{"className":13684},[2673],[28,13686,13689,13707,13716,13725],{"className":13687,"style":13688},[2677],"height:3.1em;",[28,13690,13692,13695],{"style":13691},"top:-5.26em;",[28,13693],{"className":13694,"style":9357},[2685],[28,13696,13698,13701,13704],{"className":13697},[79],[28,13699,1701],{"className":13700},[1385],[28,13702],{"className":13703,"style":90},[89],[28,13705,11002],{"className":13706,"style":4471},[79,80],[28,13708,13710,13713],{"style":13709},"top:-3.76em;",[28,13711],{"className":13712,"style":9357},[2685],[28,13714],{"className":13715},[79],[28,13717,13719,13722],{"style":13718},"top:-2.26em;",[28,13720],{"className":13721,"style":9357},[2685],[28,13723],{"className":13724},[79],[28,13726,13728,13731],{"style":13727},"top:-0.76em;",[28,13729],{"className":13730,"style":9357},[2685],[28,13732],{"className":13733},[79],[28,13735,2701],{"className":13736},[2700],[28,13738,13740],{"className":13739},[2673],[28,13741,13744],{"className":13742,"style":13743},[2677],"height:2.6em;",[28,13745],{},[28,13747,13750],{"className":13748},[13749],"col-align-l",[28,13751,13753,14077],{"className":13752},[2668,2669],[28,13754,13756,14074],{"className":13755},[2673],[28,13757,13759,13894,13971,14036],{"className":13758,"style":13688},[2677],[28,13760,13761,13764],{"style":13691},[28,13762],{"className":13763,"style":9357},[2685],[28,13765,13767,13770,13773,13776,13779,13782,13785,13788,13791,13794,13797,13800,13803,13806,13809,13812,13815,13818,13821,13824,13827,13891],{"className":13766},[79],[28,13768],{"className":13769},[79],[28,13771],{"className":13772,"style":140},[89],[28,13774,282],{"className":13775},[144],[28,13777],{"className":13778,"style":140},[89],[28,13780,1710],{"className":13781},[356],[28,13783,11123],{"className":13784,"style":11155},[79,80],[28,13786],{"className":13787,"style":140},[89],[28,13789,203],{"className":13790},[144],[28,13792],{"className":13793,"style":140},[89],[28,13795,10536],{"className":13796,"style":10583},[79,80],[28,13798],{"className":13799,"style":140},[89],[28,13801,1719],{"className":13802},[144],[28,13804],{"className":13805,"style":140},[89],[28,13807,11002],{"className":13808,"style":4471},[79,80],[28,13810,269],{"className":13811},[356],[28,13813,11123],{"className":13814,"style":11155},[79,80],[28,13816,279],{"className":13817},[383],[28,13819],{"className":13820,"style":140},[89],[28,13822,282],{"className":13823},[144],[28,13825],{"className":13826,"style":140},[89],[28,13828,13830,13833],{"className":13829},[79],[28,13831,1733],{"className":13832},[79],[28,13834,13836],{"className":13835},[2664],[28,13837,13839,13882],{"className":13838},[2668,2669],[28,13840,13842,13879],{"className":13841},[2673],[28,13843,13846],{"className":13844,"style":13845},[2677],"height:0.3448em;",[28,13847,13849,13852],{"style":13848},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[28,13850],{"className":13851,"style":2686},[2685],[28,13853,13855],{"className":13854},[2690,2691,2692,2693],[28,13856,13858,13861,13864,13867,13870,13873,13876],{"className":13857},[79,2693],[28,13859,269],{"className":13860},[356,2693],[28,13862,7634],{"className":13863,"style":7654},[79,80,2693],[28,13865,274],{"className":13866},[367,2693],[28,13868,10536],{"className":13869,"style":10583},[79,80,2693],[28,13871,279],{"className":13872},[383,2693],[28,13874,7699],{"className":13875},[79,2693],[28,13877,7634],{"className":13878,"style":7654},[79,80,2693],[28,13880,2701],{"className":13881},[2700],[28,13883,13885],{"className":13884},[2673],[28,13886,13889],{"className":13887,"style":13888},[2677],"height:0.3552em;",[28,13890],{},[28,13892,1736],{"className":13893},[383],[28,13895,13896,13899],{"style":13709},[28,13897],{"className":13898,"style":9357},[2685],[28,13900,13902,13905,13908,13911,13914,13917,13920,13923,13926,13929,13932,13935,13938,13941,13944,13947,13950,13953,13956,13959,13962,13965,13968],{"className":13901},[79],[28,13903],{"className":13904},[79],[28,13906],{"className":13907,"style":140},[89],[28,13909,282],{"className":13910},[144],[28,13912],{"className":13913,"style":140},[89],[28,13915,1710],{"className":13916},[356],[28,13918,11123],{"className":13919,"style":11155},[79,80],[28,13921],{"className":13922,"style":140},[89],[28,13924,203],{"className":13925},[144],[28,13927],{"className":13928,"style":140},[89],[28,13930,10536],{"className":13931,"style":10583},[79,80],[28,13933],{"className":13934,"style":140},[89],[28,13936,1719],{"className":13937},[144],[28,13939],{"className":13940,"style":140},[89],[28,13942,11123],{"className":13943,"style":11155},[79,80],[28,13945],{"className":13946,"style":363},[89],[28,13948,274],{"className":13949},[367],[28,13951],{"className":13952,"style":363},[89],[28,13954,7634],{"className":13955,"style":7654},[79,80],[28,13957],{"className":13958,"style":140},[89],[28,13960,282],{"className":13961},[144],[28,13963],{"className":13964,"style":140},[89],[28,13966,7634],{"className":13967,"style":7654},[79,80],[28,13969,1736],{"className":13970},[383],[28,13972,13973,13976],{"style":13718},[28,13974],{"className":13975,"style":9357},[2685],[28,13977,13979,13982,13985,13988,13991,13994,13997,14000,14003,14006,14009,14012,14015,14018,14021,14024,14027,14030,14033],{"className":13978},[79],[28,13980],{"className":13981},[79],[28,13983],{"className":13984,"style":140},[89],[28,13986,282],{"className":13987},[144],[28,13989],{"className":13990,"style":140},[89],[28,13992,1710],{"className":13993},[356],[28,13995,11123],{"className":13996,"style":11155},[79,80],[28,13998],{"className":13999,"style":140},[89],[28,14001,203],{"className":14002},[144],[28,14004],{"className":14005,"style":140},[89],[28,14007,10536],{"className":14008,"style":10583},[79,80],[28,14010],{"className":14011,"style":140},[89],[28,14013,1719],{"className":14014},[144],[28,14016],{"className":14017,"style":140},[89],[28,14019,11123],{"className":14020,"style":11155},[79,80],[28,14022],{"className":14023,"style":140},[89],[28,14025,203],{"className":14026},[144],[28,14028],{"className":14029,"style":140},[89],[28,14031,7634],{"className":14032,"style":7654},[79,80],[28,14034,1736],{"className":14035},[383],[28,14037,14038,14041],{"style":13727},[28,14039],{"className":14040,"style":9357},[2685],[28,14042,14044,14047,14050,14053,14056,14059,14062,14065,14068,14071],{"className":14043},[79],[28,14045],{"className":14046},[79],[28,14048],{"className":14049,"style":140},[89],[28,14051,282],{"className":14052},[144],[28,14054],{"className":14055,"style":140},[89],[28,14057,10536],{"className":14058,"style":10583},[79,80],[28,14060],{"className":14061,"style":363},[89],[28,14063,10630],{"className":14064},[367],[28,14066],{"className":14067,"style":363},[89],[28,14069,7634],{"className":14070,"style":7654},[79,80],[28,14072,336],{"className":14073},[79],[28,14075,2701],{"className":14076},[2700],[28,14078,14080],{"className":14079},[2673],[28,14081,14083],{"className":14082,"style":13743},[2677],[28,14084],{},[545,14086,14087,14090,14091,3062,14119,14206,14207,14342,14343],{},[23,14088,14089],{},"应用第一同态定理",":\n根据定理 3.3.3，对于满同态 ",[28,14092,14094,14107],{"className":14093},[31],[28,14095,14097],{"className":14096},[35],[37,14098,14099],{"xmlns":39},[41,14100,14101,14105],{},[44,14102,14103],{},[47,14104,11002],{},[59,14106,12833],{"encoding":61},[28,14108,14110],{"className":14109,"ariaHidden":53},[66],[28,14111,14113,14116],{"className":14112},[70],[28,14114],{"className":14115,"style":133},[74],[28,14117,11002],{"className":14118,"style":4471},[79,80],[28,14120,14122,14152],{"className":14121},[31],[28,14123,14125],{"className":14124},[35],[37,14126,14127],{"xmlns":39},[41,14128,14129,14149],{},[44,14130,14131,14133,14135,14137,14139,14141,14143,14145,14147],{},[47,14132,10536],{},[47,14134,7699],{"mathvariant":191},[47,14136,1701],{},[51,14138,1363],{},[47,14140,11002],{},[51,14142,1166],{},[47,14144,1864],{"mathvariant":191},[51,14146,1363],{},[47,14148,11002],{},[59,14150,14151],{"encoding":61},"K \u002F \\ker \\psi \\cong \\operatorname{Im} \\psi",[28,14153,14155,14188],{"className":14154,"ariaHidden":53},[66],[28,14156,14158,14161,14164,14167,14170,14173,14176,14179,14182,14185],{"className":14157},[70],[28,14159],{"className":14160,"style":349},[74],[28,14162,10536],{"className":14163,"style":10583},[79,80],[28,14165,7699],{"className":14166},[79],[28,14168],{"className":14169,"style":90},[89],[28,14171,1701],{"className":14172},[1385],[28,14174],{"className":14175,"style":90},[89],[28,14177,11002],{"className":14178,"style":4471},[79,80],[28,14180],{"className":14181,"style":140},[89],[28,14183,1166],{"className":14184},[144],[28,14186],{"className":14187,"style":140},[89],[28,14189,14191,14194,14200,14203],{"className":14190},[70],[28,14192],{"className":14193,"style":133},[74],[28,14195,14197],{"className":14196},[1385],[28,14198,1864],{"className":14199},[79,1389],[28,14201],{"className":14202,"style":90},[89],[28,14204,11002],{"className":14205,"style":4471},[79,80],"。\n即 ",[28,14208,14210,14252],{"className":14209},[31],[28,14211,14213],{"className":14212},[35],[37,14214,14215],{"xmlns":39},[41,14216,14217,14249],{},[44,14218,14219,14221,14223,14225,14227,14229,14231,14233,14235,14237,14239,14241,14243,14245,14247],{},[47,14220,10536],{},[47,14222,7699],{"mathvariant":191},[51,14224,269],{"stretchy":268},[47,14226,7634],{},[51,14228,10630],{},[47,14230,10536],{},[51,14232,279],{"stretchy":268},[51,14234,1166],{},[51,14236,269],{"stretchy":268},[47,14238,7634],{},[51,14240,274],{},[47,14242,10536],{},[51,14244,279],{"stretchy":268},[47,14246,7699],{"mathvariant":191},[47,14248,7634],{},[59,14250,14251],{"encoding":61},"K \u002F (I \\cap K) \\cong (I+K)\u002FI",[28,14253,14255,14282,14303,14324],{"className":14254,"ariaHidden":53},[66],[28,14256,14258,14261,14264,14267,14270,14273,14276,14279],{"className":14257},[70],[28,14259],{"className":14260,"style":349},[74],[28,14262,10536],{"className":14263,"style":10583},[79,80],[28,14265,7699],{"className":14266},[79],[28,14268,269],{"className":14269},[356],[28,14271,7634],{"className":14272,"style":7654},[79,80],[28,14274],{"className":14275,"style":363},[89],[28,14277,10630],{"className":14278},[367],[28,14280],{"className":14281,"style":363},[89],[28,14283,14285,14288,14291,14294,14297,14300],{"className":14284},[70],[28,14286],{"className":14287,"style":349},[74],[28,14289,10536],{"className":14290,"style":10583},[79,80],[28,14292,279],{"className":14293},[383],[28,14295],{"className":14296,"style":140},[89],[28,14298,1166],{"className":14299},[144],[28,14301],{"className":14302,"style":140},[89],[28,14304,14306,14309,14312,14315,14318,14321],{"className":14305},[70],[28,14307],{"className":14308,"style":349},[74],[28,14310,269],{"className":14311},[356],[28,14313,7634],{"className":14314,"style":7654},[79,80],[28,14316],{"className":14317,"style":363},[89],[28,14319,274],{"className":14320},[367],[28,14322],{"className":14323,"style":363},[89],[28,14325,14327,14330,14333,14336,14339],{"className":14326},[70],[28,14328],{"className":14329,"style":349},[74],[28,14331,10536],{"className":14332,"style":10583},[79,80],[28,14334,279],{"className":14335},[383],[28,14337,7699],{"className":14338},[79],[28,14340,7634],{"className":14341,"style":7654},[79,80],"。 ",[28,14344,14346,14359],{"className":14345},[31],[28,14347,14349],{"className":14348},[35],[37,14350,14351],{"xmlns":39},[41,14352,14353,14357],{},[44,14354,14355],{},[47,14356,6532],{"mathvariant":191},[59,14358,6535],{"encoding":61},[28,14360,14362],{"className":14361,"ariaHidden":53},[66],[28,14363,14365,14368],{"className":14364},[70],[28,14366],{"className":14367,"style":6545},[74],[28,14369,6532],{"className":14370},[79,2120],[1986,14372],{},[15,14374,14376],{"id":14375},"_4-典型例子","4. 典型例子",[20,14378,14379,14382,14383,14504,14505,14588,14589,14819,14820,1432,14848,14902,14903,7580,14954,9042,15094,15268,15269,8336,15349],{},[23,14380,14381],{},"例 3.3.1.","\n(i) 典范态射 ",[28,14384,14386,14415],{"className":14385},[31],[28,14387,14389],{"className":14388},[35],[37,14390,14391],{"xmlns":39},[41,14392,14393,14412],{},[44,14394,14395,14397,14399,14403,14405],{},[47,14396,7688],{},[51,14398,113],{},[47,14400,14402],{"mathvariant":14401},"double-struck","Z",[51,14404,118],{},[2621,14406,14407,14409],{},[47,14408,14402],{"mathvariant":14401},[47,14410,14411],{},"n",[59,14413,14414],{"encoding":61},"\\pi: \\mathbb{Z} \\to \\mathbb{Z}_n",[28,14416,14418,14436,14456],{"className":14417,"ariaHidden":53},[66],[28,14419,14421,14424,14427,14430,14433],{"className":14420},[70],[28,14422],{"className":14423,"style":761},[74],[28,14425,7688],{"className":14426,"style":4471},[79,80],[28,14428],{"className":14429,"style":140},[89],[28,14431,113],{"className":14432},[144],[28,14434],{"className":14435,"style":140},[89],[28,14437,14439,14443,14447,14450,14453],{"className":14438},[70],[28,14440],{"className":14441,"style":14442},[74],"height:0.6889em;",[28,14444,14402],{"className":14445},[79,14446],"mathbb",[28,14448],{"className":14449,"style":140},[89],[28,14451,118],{"className":14452},[144],[28,14454],{"className":14455,"style":140},[89],[28,14457,14459,14463],{"className":14458},[70],[28,14460],{"className":14461,"style":14462},[74],"height:0.8389em;vertical-align:-0.15em;",[28,14464,14466,14469],{"className":14465},[79],[28,14467,14402],{"className":14468},[79,14446],[28,14470,14472],{"className":14471},[2664],[28,14473,14475,14496],{"className":14474},[2668,2669],[28,14476,14478,14493],{"className":14477},[2673],[28,14479,14482],{"className":14480,"style":14481},[2677],"height:0.1514em;",[28,14483,14484,14487],{"style":2681},[28,14485],{"className":14486,"style":2686},[2685],[28,14488,14490],{"className":14489},[2690,2691,2692,2693],[28,14491,14411],{"className":14492},[79,80,2693],[28,14494,2701],{"className":14495},[2700],[28,14497,14499],{"className":14498},[2673],[28,14500,14502],{"className":14501,"style":2708},[2677],[28,14503],{}," 是一个满的环同态。\n(ii) 设 ",[28,14506,14508,14538],{"className":14507},[31],[28,14509,14511],{"className":14510},[35],[37,14512,14513],{"xmlns":39},[41,14514,14515,14535],{},[44,14516,14517,14520,14522,14525,14527,14529,14531,14533],{},[47,14518,14519],{},"A",[51,14521,203],{},[47,14523,14524],{},"M",[51,14526,269],{"stretchy":268},[47,14528,14411],{},[51,14530,54],{"separator":53},[47,14532,49],{"mathvariant":14401},[51,14534,279],{"stretchy":268},[59,14536,14537],{"encoding":61},"A \\in M(n, \\mathbb{R})",[28,14539,14541,14560],{"className":14540,"ariaHidden":53},[66],[28,14542,14544,14548,14551,14554,14557],{"className":14543},[70],[28,14545],{"className":14546,"style":14547},[74],"height:0.7224em;vertical-align:-0.0391em;",[28,14549,14519],{"className":14550},[79,80],[28,14552],{"className":14553,"style":140},[89],[28,14555,203],{"className":14556},[144],[28,14558],{"className":14559,"style":140},[89],[28,14561,14563,14566,14570,14573,14576,14579,14582,14585],{"className":14562},[70],[28,14564],{"className":14565,"style":349},[74],[28,14567,14524],{"className":14568,"style":14569},[79,80],"margin-right:0.109em;",[28,14571,269],{"className":14572},[356],[28,14574,14411],{"className":14575},[79,80],[28,14577,54],{"className":14578},[85],[28,14580],{"className":14581,"style":90},[89],[28,14583,49],{"className":14584},[79,14446],[28,14586,279],{"className":14587},[383]," 是可逆矩阵。则 ",[28,14590,14592,14661],{"className":14591},[31],[28,14593,14595],{"className":14594},[35],[37,14596,14597],{"xmlns":39},[41,14598,14599,14658],{},[44,14600,14601,14603,14605,14607,14609,14611,14613,14615,14617,14619,14621,14623,14625,14627,14629,14631,14633,14635,14637,14640,14642,14644,14646,14648],{},[47,14602,110],{},[51,14604,113],{},[47,14606,14524],{},[51,14608,269],{"stretchy":268},[47,14610,14411],{},[51,14612,54],{"separator":53},[47,14614,49],{"mathvariant":14401},[51,14616,279],{"stretchy":268},[51,14618,118],{},[47,14620,14524],{},[51,14622,269],{"stretchy":268},[47,14624,14411],{},[51,14626,54],{"separator":53},[47,14628,49],{"mathvariant":14401},[51,14630,279],{"stretchy":268},[51,14632,54],{"separator":53},[47,14634,110],{},[51,14636,269],{"stretchy":268},[47,14638,14639],{},"X",[51,14641,279],{"stretchy":268},[51,14643,282],{},[47,14645,14519],{},[47,14647,14639],{},[6696,14649,14650,14652],{},[47,14651,14519],{},[44,14653,14654,14656],{},[51,14655,3201],{},[1731,14657,6706],{},[59,14659,14660],{"encoding":61},"\\phi: M(n, \\mathbb{R}) \\to M(n, \\mathbb{R}), \\phi(X) = AXA^{-1}",[28,14662,14664,14682,14718,14772],{"className":14663,"ariaHidden":53},[66],[28,14665,14667,14670,14673,14676,14679],{"className":14666},[70],[28,14668],{"className":14669,"style":133},[74],[28,14671,110],{"className":14672},[79,80],[28,14674],{"className":14675,"style":140},[89],[28,14677,113],{"className":14678},[144],[28,14680],{"className":14681,"style":140},[89],[28,14683,14685,14688,14691,14694,14697,14700,14703,14706,14709,14712,14715],{"className":14684},[70],[28,14686],{"className":14687,"style":349},[74],[28,14689,14524],{"className":14690,"style":14569},[79,80],[28,14692,269],{"className":14693},[356],[28,14695,14411],{"className":14696},[79,80],[28,14698,54],{"className":14699},[85],[28,14701],{"className":14702,"style":90},[89],[28,14704,49],{"className":14705},[79,14446],[28,14707,279],{"className":14708},[383],[28,14710],{"className":14711,"style":140},[89],[28,14713,118],{"className":14714},[144],[28,14716],{"className":14717,"style":140},[89],[28,14719,14721,14724,14727,14730,14733,14736,14739,14742,14745,14748,14751,14754,14757,14760,14763,14766,14769],{"className":14720},[70],[28,14722],{"className":14723,"style":349},[74],[28,14725,14524],{"className":14726,"style":14569},[79,80],[28,14728,269],{"className":14729},[356],[28,14731,14411],{"className":14732},[79,80],[28,14734,54],{"className":14735},[85],[28,14737],{"className":14738,"style":90},[89],[28,14740,49],{"className":14741},[79,14446],[28,14743,279],{"className":14744},[383],[28,14746,54],{"className":14747},[85],[28,14749],{"className":14750,"style":90},[89],[28,14752,110],{"className":14753},[79,80],[28,14755,269],{"className":14756},[356],[28,14758,14639],{"className":14759,"style":7654},[79,80],[28,14761,279],{"className":14762},[383],[28,14764],{"className":14765,"style":140},[89],[28,14767,282],{"className":14768},[144],[28,14770],{"className":14771,"style":140},[89],[28,14773,14775,14778,14781,14784],{"className":14774},[70],[28,14776],{"className":14777,"style":6774},[74],[28,14779,14519],{"className":14780},[79,80],[28,14782,14639],{"className":14783,"style":7654},[79,80],[28,14785,14787,14790],{"className":14786},[79],[28,14788,14519],{"className":14789},[79,80],[28,14791,14793],{"className":14792},[2664],[28,14794,14796],{"className":14795},[2668],[28,14797,14799],{"className":14798},[2673],[28,14800,14802],{"className":14801,"style":6774},[2677],[28,14803,14804,14807],{"style":6777},[28,14805],{"className":14806,"style":2686},[2685],[28,14808,14810],{"className":14809},[2690,2691,2692,2693],[28,14811,14813,14816],{"className":14812},[79,2693],[28,14814,3201],{"className":14815},[79,2693],[28,14817,6706],{"className":14818},[79,2693]," 是一个环同构。称为内自同构。\n(iii) 设 ",[28,14821,14823,14836],{"className":14822},[31],[28,14824,14826],{"className":14825},[35],[37,14827,14828],{"xmlns":39},[41,14829,14830,14834],{},[44,14831,14832],{},[47,14833,49],{},[59,14835,49],{"encoding":61},[28,14837,14839],{"className":14838,"ariaHidden":53},[66],[28,14840,14842,14845],{"className":14841},[70],[28,14843],{"className":14844,"style":154},[74],[28,14846,49],{"className":14847,"style":81},[79,80],[28,14849,14851,14875],{"className":14850},[31],[28,14852,14854],{"className":14853},[35],[37,14855,14856],{"xmlns":39},[41,14857,14858,14872],{},[44,14859,14860,14863,14865,14867,14869],{},[51,14861,14862],{"stretchy":268},"[",[1731,14864,1733],{},[51,14866,54],{"separator":53},[1731,14868,6706],{},[51,14870,14871],{"stretchy":268},"]",[59,14873,14874],{"encoding":61},"[0, 1]",[28,14876,14878],{"className":14877,"ariaHidden":53},[66],[28,14879,14881,14884,14887,14890,14893,14896,14899],{"className":14880},[70],[28,14882],{"className":14883,"style":349},[74],[28,14885,14862],{"className":14886},[356],[28,14888,1733],{"className":14889},[79],[28,14891,54],{"className":14892},[85],[28,14894],{"className":14895,"style":90},[89],[28,14897,6706],{"className":14898},[79],[28,14900,14871],{"className":14901},[383]," 上的连续实函数环， ",[28,14904,14906,14924],{"className":14905},[31],[28,14907,14909],{"className":14908},[35],[37,14910,14911],{"xmlns":39},[41,14912,14913,14921],{},[44,14914,14915,14917,14919],{},[47,14916,195],{},[51,14918,203],{},[47,14920,49],{"mathvariant":14401},[59,14922,14923],{"encoding":61},"a \\in \\mathbb{R}",[28,14925,14927,14945],{"className":14926,"ariaHidden":53},[66],[28,14928,14930,14933,14936,14939,14942],{"className":14929},[70],[28,14931],{"className":14932,"style":1960},[74],[28,14934,195],{"className":14935},[79,80],[28,14937],{"className":14938,"style":140},[89],[28,14940,203],{"className":14941},[144],[28,14943],{"className":14944,"style":140},[89],[28,14946,14948,14951],{"className":14947},[70],[28,14949],{"className":14950,"style":14442},[74],[28,14952,49],{"className":14953},[79,14446],[28,14955,14957,15000],{"className":14956},[31],[28,14958,14960],{"className":14959},[35],[37,14961,14962],{"xmlns":39},[41,14963,14964,14997],{},[44,14965,14966,14968,14970,14972,14974,14976,14978,14980,14982,14985,14987,14989,14991,14993,14995],{},[47,14967,110],{},[51,14969,113],{},[47,14971,49],{},[51,14973,118],{},[47,14975,49],{"mathvariant":14401},[51,14977,54],{"separator":53},[47,14979,110],{},[51,14981,269],{"stretchy":268},[47,14983,14984],{},"f",[51,14986,279],{"stretchy":268},[51,14988,282],{},[47,14990,14984],{},[51,14992,269],{"stretchy":268},[47,14994,195],{},[51,14996,279],{"stretchy":268},[59,14998,14999],{"encoding":61},"\\phi: R \\to \\mathbb{R}, \\phi(f) = f(a)",[28,15001,15003,15021,15039,15076],{"className":15002,"ariaHidden":53},[66],[28,15004,15006,15009,15012,15015,15018],{"className":15005},[70],[28,15007],{"className":15008,"style":133},[74],[28,15010,110],{"className":15011},[79,80],[28,15013],{"className":15014,"style":140},[89],[28,15016,113],{"className":15017},[144],[28,15019],{"className":15020,"style":140},[89],[28,15022,15024,15027,15030,15033,15036],{"className":15023},[70],[28,15025],{"className":15026,"style":154},[74],[28,15028,49],{"className":15029,"style":81},[79,80],[28,15031],{"className":15032,"style":140},[89],[28,15034,118],{"className":15035},[144],[28,15037],{"className":15038,"style":140},[89],[28,15040,15042,15045,15048,15051,15054,15057,15060,15064,15067,15070,15073],{"className":15041},[70],[28,15043],{"className":15044,"style":349},[74],[28,15046,49],{"className":15047},[79,14446],[28,15049,54],{"className":15050},[85],[28,15052],{"className":15053,"style":90},[89],[28,15055,110],{"className":15056},[79,80],[28,15058,269],{"className":15059},[356],[28,15061,14984],{"className":15062,"style":15063},[79,80],"margin-right:0.1076em;",[28,15065,279],{"className":15066},[383],[28,15068],{"className":15069,"style":140},[89],[28,15071,282],{"className":15072},[144],[28,15074],{"className":15075,"style":140},[89],[28,15077,15079,15082,15085,15088,15091],{"className":15078},[70],[28,15080],{"className":15081,"style":349},[74],[28,15083,14984],{"className":15084,"style":15063},[79,80],[28,15086,269],{"className":15087},[356],[28,15089,195],{"className":15090},[79,80],[28,15092,279],{"className":15093},[383],[28,15095,15097,15145],{"className":15096},[31],[28,15098,15100],{"className":15099},[35],[37,15101,15102],{"xmlns":39},[41,15103,15104,15142],{},[44,15105,15106,15108,15110,15112,15114,15116,15118,15120,15122,15124,15126,15128,15130,15132,15134,15136,15138,15140],{},[47,15107,1701],{},[51,15109,1363],{},[47,15111,110],{},[51,15113,282],{},[51,15115,1710],{"stretchy":268},[47,15117,14984],{},[51,15119,203],{},[47,15121,49],{},[51,15123,1719],{},[47,15125,14984],{},[51,15127,269],{"stretchy":268},[47,15129,195],{},[51,15131,279],{"stretchy":268},[51,15133,282],{},[1731,15135,1733],{},[51,15137,1736],{"stretchy":268},[51,15139,2090],{},[47,15141,49],{},[59,15143,15144],{"encoding":61},"\\ker \\phi = \\{f \\in R \\mid f(a) = 0\\} \\lhd R",[28,15146,15148,15172,15193,15211,15238,15259],{"className":15147,"ariaHidden":53},[66],[28,15149,15151,15154,15157,15160,15163,15166,15169],{"className":15150},[70],[28,15152],{"className":15153,"style":133},[74],[28,15155,1701],{"className":15156},[1385],[28,15158],{"className":15159,"style":90},[89],[28,15161,110],{"className":15162},[79,80],[28,15164],{"className":15165,"style":140},[89],[28,15167,282],{"className":15168},[144],[28,15170],{"className":15171,"style":140},[89],[28,15173,15175,15178,15181,15184,15187,15190],{"className":15174},[70],[28,15176],{"className":15177,"style":349},[74],[28,15179,1710],{"className":15180},[356],[28,15182,14984],{"className":15183,"style":15063},[79,80],[28,15185],{"className":15186,"style":140},[89],[28,15188,203],{"className":15189},[144],[28,15191],{"className":15192,"style":140},[89],[28,15194,15196,15199,15202,15205,15208],{"className":15195},[70],[28,15197],{"className":15198,"style":349},[74],[28,15200,49],{"className":15201,"style":81},[79,80],[28,15203],{"className":15204,"style":140},[89],[28,15206,1719],{"className":15207},[144],[28,15209],{"className":15210,"style":140},[89],[28,15212,15214,15217,15220,15223,15226,15229,15232,15235],{"className":15213},[70],[28,15215],{"className":15216,"style":349},[74],[28,15218,14984],{"className":15219,"style":15063},[79,80],[28,15221,269],{"className":15222},[356],[28,15224,195],{"className":15225},[79,80],[28,15227,279],{"className":15228},[383],[28,15230],{"className":15231,"style":140},[89],[28,15233,282],{"className":15234},[144],[28,15236],{"className":15237,"style":140},[89],[28,15239,15241,15244,15247,15250,15253,15256],{"className":15240},[70],[28,15242],{"className":15243,"style":349},[74],[28,15245,1733],{"className":15246},[79],[28,15248,1736],{"className":15249},[383],[28,15251],{"className":15252,"style":363},[89],[28,15254,2090],{"className":15255},[367,2120],[28,15257],{"className":15258,"style":363},[89],[28,15260,15262,15265],{"className":15261},[70],[28,15263],{"className":15264,"style":154},[74],[28,15266,49],{"className":15267,"style":81},[79,80],". 特别的， ",[28,15270,15272,15300],{"className":15271},[31],[28,15273,15275],{"className":15274},[35],[37,15276,15277],{"xmlns":39},[41,15278,15279,15297],{},[44,15280,15281,15283,15285,15287,15289,15291,15293,15295],{},[47,15282,192],{"mathvariant":191},[47,15284,57],{},[51,15286,11216],{},[51,15288,14862],{"stretchy":268},[1731,15290,1733],{},[51,15292,54],{"separator":53},[1731,15294,6706],{},[51,15296,14871],{"stretchy":268},[59,15298,15299],{"encoding":61},"\\forall S \\subseteq [0, 1]",[28,15301,15303,15325],{"className":15302,"ariaHidden":53},[66],[28,15304,15306,15310,15313,15316,15319,15322],{"className":15305},[70],[28,15307],{"className":15308,"style":15309},[74],"height:0.8304em;vertical-align:-0.136em;",[28,15311,192],{"className":15312},[79],[28,15314,57],{"className":15315,"style":94},[79,80],[28,15317],{"className":15318,"style":140},[89],[28,15320,11216],{"className":15321},[144],[28,15323],{"className":15324,"style":140},[89],[28,15326,15328,15331,15334,15337,15340,15343,15346],{"className":15327},[70],[28,15329],{"className":15330,"style":349},[74],[28,15332,14862],{"className":15333},[356],[28,15335,1733],{"className":15336},[79],[28,15338,54],{"className":15339},[85],[28,15341],{"className":15342,"style":90},[89],[28,15344,6706],{"className":15345},[79],[28,15347,14871],{"className":15348},[383],[28,15350,15352,15402],{"className":15351},[31],[28,15353,15355],{"className":15354},[35],[37,15356,15357],{"xmlns":39},[41,15358,15359,15399],{},[44,15360,15361,15367,15369,15371,15373,15375,15377,15379,15381,15383,15385,15387,15389,15391,15393,15395,15397],{},[2621,15362,15363,15365],{},[47,15364,7634],{},[47,15366,57],{},[51,15368,282],{},[51,15370,1710],{"stretchy":268},[47,15372,14984],{},[51,15374,203],{},[47,15376,49],{},[51,15378,1719],{},[47,15380,14984],{},[51,15382,269],{"stretchy":268},[47,15384,57],{},[51,15386,279],{"stretchy":268},[51,15388,282],{},[1731,15390,1733],{},[51,15392,1736],{"stretchy":268},[51,15394,2090],{},[47,15396,49],{},[47,15398,336],{"mathvariant":191},[59,15400,15401],{"encoding":61},"I_S = \\{f \\in R \\mid f(S) = 0\\} \\lhd R.",[28,15403,15405,15462,15483,15501,15528,15549],{"className":15404,"ariaHidden":53},[66],[28,15406,15408,15412,15453,15456,15459],{"className":15407},[70],[28,15409],{"className":15410,"style":15411},[74],"height:0.8333em;vertical-align:-0.15em;",[28,15413,15415,15418],{"className":15414},[79],[28,15416,7634],{"className":15417,"style":7654},[79,80],[28,15419,15421],{"className":15420},[2664],[28,15422,15424,15445],{"className":15423},[2668,2669],[28,15425,15427,15442],{"className":15426},[2673],[28,15428,15430],{"className":15429,"style":2678},[2677],[28,15431,15433,15436],{"style":15432},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[28,15434],{"className":15435,"style":2686},[2685],[28,15437,15439],{"className":15438},[2690,2691,2692,2693],[28,15440,57],{"className":15441,"style":94},[79,80,2693],[28,15443,2701],{"className":15444},[2700],[28,15446,15448],{"className":15447},[2673],[28,15449,15451],{"className":15450,"style":2708},[2677],[28,15452],{},[28,15454],{"className":15455,"style":140},[89],[28,15457,282],{"className":15458},[144],[28,15460],{"className":15461,"style":140},[89],[28,15463,15465,15468,15471,15474,15477,15480],{"className":15464},[70],[28,15466],{"className":15467,"style":349},[74],[28,15469,1710],{"className":15470},[356],[28,15472,14984],{"className":15473,"style":15063},[79,80],[28,15475],{"className":15476,"style":140},[89],[28,15478,203],{"className":15479},[144],[28,15481],{"className":15482,"style":140},[89],[28,15484,15486,15489,15492,15495,15498],{"className":15485},[70],[28,15487],{"className":15488,"style":349},[74],[28,15490,49],{"className":15491,"style":81},[79,80],[28,15493],{"className":15494,"style":140},[89],[28,15496,1719],{"className":15497},[144],[28,15499],{"className":15500,"style":140},[89],[28,15502,15504,15507,15510,15513,15516,15519,15522,15525],{"className":15503},[70],[28,15505],{"className":15506,"style":349},[74],[28,15508,14984],{"className":15509,"style":15063},[79,80],[28,15511,269],{"className":15512},[356],[28,15514,57],{"className":15515,"style":94},[79,80],[28,15517,279],{"className":15518},[383],[28,15520],{"className":15521,"style":140},[89],[28,15523,282],{"className":15524},[144],[28,15526],{"className":15527,"style":140},[89],[28,15529,15531,15534,15537,15540,15543,15546],{"className":15530},[70],[28,15532],{"className":15533,"style":349},[74],[28,15535,1733],{"className":15536},[79],[28,15538,1736],{"className":15539},[383],[28,15541],{"className":15542,"style":363},[89],[28,15544,2090],{"className":15545},[367,2120],[28,15547],{"className":15548,"style":363},[89],[28,15550,15552,15555,15558],{"className":15551},[70],[28,15553],{"className":15554,"style":154},[74],[28,15556,49],{"className":15557,"style":81},[79,80],[28,15559,336],{"className":15560},[79],[1986,15562],{},[15,15564,15566],{"id":15565},"_5-理想的互素与积","5. 理想的互素与积",[20,15568,15569,26,15572,15636,15637,15710,15711,6554,15753,537],{},[23,15570,15571],{},"定义 3.3.2.",[28,15573,15575,15597],{"className":15574},[31],[28,15576,15578],{"className":15577},[35],[37,15579,15580],{"xmlns":39},[41,15581,15582,15594],{},[44,15583,15584,15586,15588,15590,15592],{},[47,15585,7634],{},[51,15587,54],{"separator":53},[47,15589,6642],{},[51,15591,2090],{},[47,15593,49],{},[59,15595,15596],{"encoding":61},"I, J \\lhd R",[28,15598,15600,15627],{"className":15599,"ariaHidden":53},[66],[28,15601,15603,15606,15609,15612,15615,15618,15621,15624],{"className":15602},[70],[28,15604],{"className":15605,"style":75},[74],[28,15607,7634],{"className":15608,"style":7654},[79,80],[28,15610,54],{"className":15611},[85],[28,15613],{"className":15614,"style":90},[89],[28,15616,6642],{"className":15617,"style":6663},[79,80],[28,15619],{"className":15620,"style":363},[89],[28,15622,2090],{"className":15623},[367,2120],[28,15625],{"className":15626,"style":363},[89],[28,15628,15630,15633],{"className":15629},[70],[28,15631],{"className":15632,"style":154},[74],[28,15634,49],{"className":15635,"style":81},[79,80],". 如果 ",[28,15638,15640,15662],{"className":15639},[31],[28,15641,15643],{"className":15642},[35],[37,15644,15645],{"xmlns":39},[41,15646,15647,15659],{},[44,15648,15649,15651,15653,15655,15657],{},[47,15650,7634],{},[51,15652,274],{},[47,15654,6642],{},[51,15656,282],{},[47,15658,49],{},[59,15660,15661],{"encoding":61},"I+J=R",[28,15663,15665,15683,15701],{"className":15664,"ariaHidden":53},[66],[28,15666,15668,15671,15674,15677,15680],{"className":15667},[70],[28,15669],{"className":15670,"style":10649},[74],[28,15672,7634],{"className":15673,"style":7654},[79,80],[28,15675],{"className":15676,"style":363},[89],[28,15678,274],{"className":15679},[367],[28,15681],{"className":15682,"style":363},[89],[28,15684,15686,15689,15692,15695,15698],{"className":15685},[70],[28,15687],{"className":15688,"style":154},[74],[28,15690,6642],{"className":15691,"style":6663},[79,80],[28,15693],{"className":15694,"style":140},[89],[28,15696,282],{"className":15697},[144],[28,15699],{"className":15700,"style":140},[89],[28,15702,15704,15707],{"className":15703},[70],[28,15705],{"className":15706,"style":154},[74],[28,15708,49],{"className":15709,"style":81},[79,80],", 则称 ",[28,15712,15714,15732],{"className":15713},[31],[28,15715,15717],{"className":15716},[35],[37,15718,15719],{"xmlns":39},[41,15720,15721,15729],{},[44,15722,15723,15725,15727],{},[47,15724,7634],{},[51,15726,54],{"separator":53},[47,15728,6642],{},[59,15730,15731],{"encoding":61},"I, J",[28,15733,15735],{"className":15734,"ariaHidden":53},[66],[28,15736,15738,15741,15744,15747,15750],{"className":15737},[70],[28,15739],{"className":15740,"style":75},[74],[28,15742,7634],{"className":15743,"style":7654},[79,80],[28,15745,54],{"className":15746},[85],[28,15748],{"className":15749,"style":90},[89],[28,15751,6642],{"className":15752,"style":6663},[79,80],[23,15754,15755],{},"互素",[20,15757,15758,26,15761,15789,15790,6682,15853,15894,15895,15983,15984,6907,16059,16061,550,16089,16161,16162,16190,16191,16287,16288,949,16373,3180,16446,16474,16475,15983,16560,6682,16632,16705,16706,3062,16757,13298,16875,16926,16927,17000,17001,17073,17074,17115,17116],{},[23,15759,15760],{},"命题 3.3.3.",[28,15762,15764,15777],{"className":15763},[31],[28,15765,15767],{"className":15766},[35],[37,15768,15769],{"xmlns":39},[41,15770,15771,15775],{},[44,15772,15773],{},[47,15774,49],{},[59,15776,49],{"encoding":61},[28,15778,15780],{"className":15779,"ariaHidden":53},[66],[28,15781,15783,15786],{"className":15782},[70],[28,15784],{"className":15785,"style":154},[74],[28,15787,49],{"className":15788,"style":81},[79,80]," 是幺环, ",[28,15791,15793,15814],{"className":15792},[31],[28,15794,15796],{"className":15795},[35],[37,15797,15798],{"xmlns":39},[41,15799,15800,15812],{},[44,15801,15802,15804,15806,15808,15810],{},[47,15803,7634],{},[51,15805,54],{"separator":53},[47,15807,6642],{},[51,15809,2090],{},[47,15811,49],{},[59,15813,15596],{"encoding":61},[28,15815,15817,15844],{"className":15816,"ariaHidden":53},[66],[28,15818,15820,15823,15826,15829,15832,15835,15838,15841],{"className":15819},[70],[28,15821],{"className":15822,"style":75},[74],[28,15824,7634],{"className":15825,"style":7654},[79,80],[28,15827,54],{"className":15828},[85],[28,15830],{"className":15831,"style":90},[89],[28,15833,6642],{"className":15834,"style":6663},[79,80],[28,15836],{"className":15837,"style":363},[89],[28,15839,2090],{"className":15840},[367,2120],[28,15842],{"className":15843,"style":363},[89],[28,15845,15847,15850],{"className":15846},[70],[28,15848],{"className":15849,"style":154},[74],[28,15851,49],{"className":15852,"style":81},[79,80],[28,15854,15856,15873],{"className":15855},[31],[28,15857,15859],{"className":15858},[35],[37,15860,15861],{"xmlns":39},[41,15862,15863,15871],{},[44,15864,15865,15867,15869],{},[47,15866,7634],{},[51,15868,54],{"separator":53},[47,15870,6642],{},[59,15872,15731],{"encoding":61},[28,15874,15876],{"className":15875,"ariaHidden":53},[66],[28,15877,15879,15882,15885,15888,15891],{"className":15878},[70],[28,15880],{"className":15881,"style":75},[74],[28,15883,7634],{"className":15884,"style":7654},[79,80],[28,15886,54],{"className":15887},[85],[28,15889],{"className":15890,"style":90},[89],[28,15892,6642],{"className":15893,"style":6663},[79,80]," 互素，当且仅当存在 ",[28,15896,15898,15925],{"className":15897},[31],[28,15899,15901],{"className":15900},[35],[37,15902,15903],{"xmlns":39},[41,15904,15905,15922],{},[44,15906,15907,15909,15911,15913,15915,15918,15920],{},[47,15908,12938],{},[51,15910,203],{},[47,15912,7634],{},[51,15914,54],{"separator":53},[47,15916,15917],{},"j",[51,15919,203],{},[47,15921,6642],{},[59,15923,15924],{"encoding":61},"i \\in I, j \\in J",[28,15926,15928,15946,15974],{"className":15927,"ariaHidden":53},[66],[28,15929,15931,15934,15937,15940,15943],{"className":15930},[70],[28,15932],{"className":15933,"style":13045},[74],[28,15935,12938],{"className":15936},[79,80],[28,15938],{"className":15939,"style":140},[89],[28,15941,203],{"className":15942},[144],[28,15944],{"className":15945,"style":140},[89],[28,15947,15949,15952,15955,15958,15961,15965,15968,15971],{"className":15948},[70],[28,15950],{"className":15951,"style":75},[74],[28,15953,7634],{"className":15954,"style":7654},[79,80],[28,15956,54],{"className":15957},[85],[28,15959],{"className":15960,"style":90},[89],[28,15962,15917],{"className":15963,"style":15964},[79,80],"margin-right:0.0572em;",[28,15966],{"className":15967,"style":140},[89],[28,15969,203],{"className":15970},[144],[28,15972],{"className":15973,"style":140},[89],[28,15975,15977,15980],{"className":15976},[70],[28,15978],{"className":15979,"style":154},[74],[28,15981,6642],{"className":15982,"style":6663},[79,80],", 使得 ",[28,15985,15987,16009],{"className":15986},[31],[28,15988,15990],{"className":15989},[35],[37,15991,15992],{"xmlns":39},[41,15993,15994,16006],{},[44,15995,15996,15998,16000,16002,16004],{},[1731,15997,6706],{},[51,15999,282],{},[47,16001,12938],{},[51,16003,274],{},[47,16005,15917],{},[59,16007,16008],{"encoding":61},"1 = i+j",[28,16010,16012,16030,16049],{"className":16011,"ariaHidden":53},[66],[28,16013,16015,16018,16021,16024,16027],{"className":16014},[70],[28,16016],{"className":16017,"style":3176},[74],[28,16019,6706],{"className":16020},[79],[28,16022],{"className":16023,"style":140},[89],[28,16025,282],{"className":16026},[144],[28,16028],{"className":16029,"style":140},[89],[28,16031,16033,16037,16040,16043,16046],{"className":16032},[70],[28,16034],{"className":16035,"style":16036},[74],"height:0.7429em;vertical-align:-0.0833em;",[28,16038,12938],{"className":16039},[79,80],[28,16041],{"className":16042,"style":363},[89],[28,16044,274],{"className":16045},[367],[28,16047],{"className":16048,"style":363},[89],[28,16050,16052,16056],{"className":16051},[70],[28,16053],{"className":16054,"style":16055},[74],"height:0.854em;vertical-align:-0.1944em;",[28,16057,15917],{"className":16058,"style":15964},[79,80],[23,16060,6910],{},[28,16062,16064,16077],{"className":16063},[31],[28,16065,16067],{"className":16066},[35],[37,16068,16069],{"xmlns":39},[41,16070,16071,16075],{},[44,16072,16073],{},[51,16074,5363],{},[59,16076,5366],{"encoding":61},[28,16078,16080],{"className":16079,"ariaHidden":53},[66],[28,16081,16083,16086],{"className":16082},[70],[28,16084],{"className":16085,"style":5376},[74],[28,16087,5363],{"className":16088},[144],[28,16090,16092,16113],{"className":16091},[31],[28,16093,16095],{"className":16094},[35],[37,16096,16097],{"xmlns":39},[41,16098,16099,16111],{},[44,16100,16101,16103,16105,16107,16109],{},[47,16102,7634],{},[51,16104,274],{},[47,16106,6642],{},[51,16108,282],{},[47,16110,49],{},[59,16112,15661],{"encoding":61},[28,16114,16116,16134,16152],{"className":16115,"ariaHidden":53},[66],[28,16117,16119,16122,16125,16128,16131],{"className":16118},[70],[28,16120],{"className":16121,"style":10649},[74],[28,16123,7634],{"className":16124,"style":7654},[79,80],[28,16126],{"className":16127,"style":363},[89],[28,16129,274],{"className":16130},[367],[28,16132],{"className":16133,"style":363},[89],[28,16135,16137,16140,16143,16146,16149],{"className":16136},[70],[28,16138],{"className":16139,"style":154},[74],[28,16141,6642],{"className":16142,"style":6663},[79,80],[28,16144],{"className":16145,"style":140},[89],[28,16147,282],{"className":16148},[144],[28,16150],{"className":16151,"style":140},[89],[28,16153,16155,16158],{"className":16154},[70],[28,16156],{"className":16157,"style":154},[74],[28,16159,49],{"className":16160,"style":81},[79,80],"，因为 ",[28,16163,16165,16178],{"className":16164},[31],[28,16166,16168],{"className":16167},[35],[37,16169,16170],{"xmlns":39},[41,16171,16172,16176],{},[44,16173,16174],{},[47,16175,49],{},[59,16177,49],{"encoding":61},[28,16179,16181],{"className":16180,"ariaHidden":53},[66],[28,16182,16184,16187],{"className":16183},[70],[28,16185],{"className":16186,"style":154},[74],[28,16188,49],{"className":16189,"style":81},[79,80]," 是幺环，",[28,16192,16194,16220],{"className":16193},[31],[28,16195,16197],{"className":16196},[35],[37,16198,16199],{"xmlns":39},[41,16200,16201,16217],{},[44,16202,16203,16205,16207,16209,16211,16213,16215],{},[1731,16204,6706],{},[51,16206,203],{},[47,16208,49],{},[51,16210,282],{},[47,16212,7634],{},[51,16214,274],{},[47,16216,6642],{},[59,16218,16219],{"encoding":61},"1 \\in R = I+J",[28,16221,16223,16242,16260,16278],{"className":16222,"ariaHidden":53},[66],[28,16224,16226,16230,16233,16236,16239],{"className":16225},[70],[28,16227],{"className":16228,"style":16229},[74],"height:0.6835em;vertical-align:-0.0391em;",[28,16231,6706],{"className":16232},[79],[28,16234],{"className":16235,"style":140},[89],[28,16237,203],{"className":16238},[144],[28,16240],{"className":16241,"style":140},[89],[28,16243,16245,16248,16251,16254,16257],{"className":16244},[70],[28,16246],{"className":16247,"style":154},[74],[28,16249,49],{"className":16250,"style":81},[79,80],[28,16252],{"className":16253,"style":140},[89],[28,16255,282],{"className":16256},[144],[28,16258],{"className":16259,"style":140},[89],[28,16261,16263,16266,16269,16272,16275],{"className":16262},[70],[28,16264],{"className":16265,"style":10649},[74],[28,16267,7634],{"className":16268,"style":7654},[79,80],[28,16270],{"className":16271,"style":363},[89],[28,16273,274],{"className":16274},[367],[28,16276],{"className":16277,"style":363},[89],[28,16279,16281,16284],{"className":16280},[70],[28,16282],{"className":16283,"style":154},[74],[28,16285,6642],{"className":16286,"style":6663},[79,80],"。故存在 ",[28,16289,16291,16316],{"className":16290},[31],[28,16292,16294],{"className":16293},[35],[37,16295,16296],{"xmlns":39},[41,16297,16298,16314],{},[44,16299,16300,16302,16304,16306,16308,16310,16312],{},[47,16301,12938],{},[51,16303,203],{},[47,16305,7634],{},[51,16307,54],{"separator":53},[47,16309,15917],{},[51,16311,203],{},[47,16313,6642],{},[59,16315,15924],{"encoding":61},[28,16317,16319,16337,16364],{"className":16318,"ariaHidden":53},[66],[28,16320,16322,16325,16328,16331,16334],{"className":16321},[70],[28,16323],{"className":16324,"style":13045},[74],[28,16326,12938],{"className":16327},[79,80],[28,16329],{"className":16330,"style":140},[89],[28,16332,203],{"className":16333},[144],[28,16335],{"className":16336,"style":140},[89],[28,16338,16340,16343,16346,16349,16352,16355,16358,16361],{"className":16339},[70],[28,16341],{"className":16342,"style":75},[74],[28,16344,7634],{"className":16345,"style":7654},[79,80],[28,16347,54],{"className":16348},[85],[28,16350],{"className":16351,"style":90},[89],[28,16353,15917],{"className":16354,"style":15964},[79,80],[28,16356],{"className":16357,"style":140},[89],[28,16359,203],{"className":16360},[144],[28,16362],{"className":16363,"style":140},[89],[28,16365,16367,16370],{"className":16366},[70],[28,16368],{"className":16369,"style":154},[74],[28,16371,6642],{"className":16372,"style":6663},[79,80],[28,16374,16376,16398],{"className":16375},[31],[28,16377,16379],{"className":16378},[35],[37,16380,16381],{"xmlns":39},[41,16382,16383,16395],{},[44,16384,16385,16387,16389,16391,16393],{},[1731,16386,6706],{},[51,16388,282],{},[47,16390,12938],{},[51,16392,274],{},[47,16394,15917],{},[59,16396,16397],{"encoding":61},"1=i+j",[28,16399,16401,16419,16437],{"className":16400,"ariaHidden":53},[66],[28,16402,16404,16407,16410,16413,16416],{"className":16403},[70],[28,16405],{"className":16406,"style":3176},[74],[28,16408,6706],{"className":16409},[79],[28,16411],{"className":16412,"style":140},[89],[28,16414,282],{"className":16415},[144],[28,16417],{"className":16418,"style":140},[89],[28,16420,16422,16425,16428,16431,16434],{"className":16421},[70],[28,16423],{"className":16424,"style":16036},[74],[28,16426,12938],{"className":16427},[79,80],[28,16429],{"className":16430,"style":363},[89],[28,16432,274],{"className":16433},[367],[28,16435],{"className":16436,"style":363},[89],[28,16438,16440,16443],{"className":16439},[70],[28,16441],{"className":16442,"style":16055},[74],[28,16444,15917],{"className":16445,"style":15964},[79,80],[28,16447,16449,16462],{"className":16448},[31],[28,16450,16452],{"className":16451},[35],[37,16453,16454],{"xmlns":39},[41,16455,16456,16460],{},[44,16457,16458],{},[51,16459,5781],{},[59,16461,5784],{"encoding":61},[28,16463,16465],{"className":16464,"ariaHidden":53},[66],[28,16466,16468,16471],{"className":16467},[70],[28,16469],{"className":16470,"style":5376},[74],[28,16472,5781],{"className":16473},[144],": 若存在 ",[28,16476,16478,16503],{"className":16477},[31],[28,16479,16481],{"className":16480},[35],[37,16482,16483],{"xmlns":39},[41,16484,16485,16501],{},[44,16486,16487,16489,16491,16493,16495,16497,16499],{},[47,16488,12938],{},[51,16490,203],{},[47,16492,7634],{},[51,16494,54],{"separator":53},[47,16496,15917],{},[51,16498,203],{},[47,16500,6642],{},[59,16502,15924],{"encoding":61},[28,16504,16506,16524,16551],{"className":16505,"ariaHidden":53},[66],[28,16507,16509,16512,16515,16518,16521],{"className":16508},[70],[28,16510],{"className":16511,"style":13045},[74],[28,16513,12938],{"className":16514},[79,80],[28,16516],{"className":16517,"style":140},[89],[28,16519,203],{"className":16520},[144],[28,16522],{"className":16523,"style":140},[89],[28,16525,16527,16530,16533,16536,16539,16542,16545,16548],{"className":16526},[70],[28,16528],{"className":16529,"style":75},[74],[28,16531,7634],{"className":16532,"style":7654},[79,80],[28,16534,54],{"className":16535},[85],[28,16537],{"className":16538,"style":90},[89],[28,16540,15917],{"className":16541,"style":15964},[79,80],[28,16543],{"className":16544,"style":140},[89],[28,16546,203],{"className":16547},[144],[28,16549],{"className":16550,"style":140},[89],[28,16552,16554,16557],{"className":16553},[70],[28,16555],{"className":16556,"style":154},[74],[28,16558,6642],{"className":16559,"style":6663},[79,80],[28,16561,16563,16584],{"className":16562},[31],[28,16564,16566],{"className":16565},[35],[37,16567,16568],{"xmlns":39},[41,16569,16570,16582],{},[44,16571,16572,16574,16576,16578,16580],{},[1731,16573,6706],{},[51,16575,282],{},[47,16577,12938],{},[51,16579,274],{},[47,16581,15917],{},[59,16583,16008],{"encoding":61},[28,16585,16587,16605,16623],{"className":16586,"ariaHidden":53},[66],[28,16588,16590,16593,16596,16599,16602],{"className":16589},[70],[28,16591],{"className":16592,"style":3176},[74],[28,16594,6706],{"className":16595},[79],[28,16597],{"className":16598,"style":140},[89],[28,16600,282],{"className":16601},[144],[28,16603],{"className":16604,"style":140},[89],[28,16606,16608,16611,16614,16617,16620],{"className":16607},[70],[28,16609],{"className":16610,"style":16036},[74],[28,16612,12938],{"className":16613},[79,80],[28,16615],{"className":16616,"style":363},[89],[28,16618,274],{"className":16619},[367],[28,16621],{"className":16622,"style":363},[89],[28,16624,16626,16629],{"className":16625},[70],[28,16627],{"className":16628,"style":16055},[74],[28,16630,15917],{"className":16631,"style":15964},[79,80],[28,16633,16635,16657],{"className":16634},[31],[28,16636,16638],{"className":16637},[35],[37,16639,16640],{"xmlns":39},[41,16641,16642,16654],{},[44,16643,16644,16646,16648,16650,16652],{},[1731,16645,6706],{},[51,16647,203],{},[47,16649,7634],{},[51,16651,274],{},[47,16653,6642],{},[59,16655,16656],{"encoding":61},"1 \\in I+J",[28,16658,16660,16678,16696],{"className":16659,"ariaHidden":53},[66],[28,16661,16663,16666,16669,16672,16675],{"className":16662},[70],[28,16664],{"className":16665,"style":16229},[74],[28,16667,6706],{"className":16668},[79],[28,16670],{"className":16671,"style":140},[89],[28,16673,203],{"className":16674},[144],[28,16676],{"className":16677,"style":140},[89],[28,16679,16681,16684,16687,16690,16693],{"className":16680},[70],[28,16682],{"className":16683,"style":10649},[74],[28,16685,7634],{"className":16686,"style":7654},[79,80],[28,16688],{"className":16689,"style":363},[89],[28,16691,274],{"className":16692},[367],[28,16694],{"className":16695,"style":363},[89],[28,16697,16699,16702],{"className":16698},[70],[28,16700],{"className":16701,"style":154},[74],[28,16703,6642],{"className":16704,"style":6663},[79,80],". 对于任意 ",[28,16707,16709,16727],{"className":16708},[31],[28,16710,16712],{"className":16711},[35],[37,16713,16714],{"xmlns":39},[41,16715,16716,16724],{},[44,16717,16718,16720,16722],{},[47,16719,876],{},[51,16721,203],{},[47,16723,49],{},[59,16725,16726],{"encoding":61},"r \\in R",[28,16728,16730,16748],{"className":16729,"ariaHidden":53},[66],[28,16731,16733,16736,16739,16742,16745],{"className":16732},[70],[28,16734],{"className":16735,"style":1960},[74],[28,16737,876],{"className":16738,"style":930},[79,80],[28,16740],{"className":16741,"style":140},[89],[28,16743,203],{"className":16744},[144],[28,16746],{"className":16747,"style":140},[89],[28,16749,16751,16754],{"className":16750},[70],[28,16752],{"className":16753,"style":154},[74],[28,16755,49],{"className":16756,"style":81},[79,80],[28,16758,16760,16790],{"className":16759},[31],[28,16761,16763],{"className":16762},[35],[37,16764,16765],{"xmlns":39},[41,16766,16767,16787],{},[44,16768,16769,16771,16773,16775,16777,16779,16781,16783,16785],{},[47,16770,876],{},[51,16772,282],{},[47,16774,876],{},[51,16776,3732],{},[1731,16778,6706],{},[51,16780,203],{},[47,16782,7634],{},[51,16784,274],{},[47,16786,6642],{},[59,16788,16789],{"encoding":61},"r = r \\cdot 1 \\in I+J",[28,16791,16793,16811,16830,16848,16866],{"className":16792,"ariaHidden":53},[66],[28,16794,16796,16799,16802,16805,16808],{"className":16795},[70],[28,16797],{"className":16798,"style":761},[74],[28,16800,876],{"className":16801,"style":930},[79,80],[28,16803],{"className":16804,"style":140},[89],[28,16806,282],{"className":16807},[144],[28,16809],{"className":16810,"style":140},[89],[28,16812,16814,16818,16821,16824,16827],{"className":16813},[70],[28,16815],{"className":16816,"style":16817},[74],"height:0.4445em;",[28,16819,876],{"className":16820,"style":930},[79,80],[28,16822],{"className":16823,"style":363},[89],[28,16825,3732],{"className":16826},[367],[28,16828],{"className":16829,"style":363},[89],[28,16831,16833,16836,16839,16842,16845],{"className":16832},[70],[28,16834],{"className":16835,"style":16229},[74],[28,16837,6706],{"className":16838},[79],[28,16840],{"className":16841,"style":140},[89],[28,16843,203],{"className":16844},[144],[28,16846],{"className":16847,"style":140},[89],[28,16849,16851,16854,16857,16860,16863],{"className":16850},[70],[28,16852],{"className":16853,"style":10649},[74],[28,16855,7634],{"className":16856,"style":7654},[79,80],[28,16858],{"className":16859,"style":363},[89],[28,16861,274],{"className":16862},[367],[28,16864],{"className":16865,"style":363},[89],[28,16867,16869,16872],{"className":16868},[70],[28,16870],{"className":16871,"style":154},[74],[28,16873,6642],{"className":16874,"style":6663},[79,80],[28,16876,16878,16896],{"className":16877},[31],[28,16879,16881],{"className":16880},[35],[37,16882,16883],{"xmlns":39},[41,16884,16885,16893],{},[44,16886,16887,16889,16891],{},[47,16888,7634],{},[51,16890,274],{},[47,16892,6642],{},[59,16894,16895],{"encoding":61},"I+J",[28,16897,16899,16917],{"className":16898,"ariaHidden":53},[66],[28,16900,16902,16905,16908,16911,16914],{"className":16901},[70],[28,16903],{"className":16904,"style":10649},[74],[28,16906,7634],{"className":16907,"style":7654},[79,80],[28,16909],{"className":16910,"style":363},[89],[28,16912,274],{"className":16913},[367],[28,16915],{"className":16916,"style":363},[89],[28,16918,16920,16923],{"className":16919},[70],[28,16921],{"className":16922,"style":154},[74],[28,16924,6642],{"className":16925,"style":6663},[79,80]," 是理想）。因此 ",[28,16928,16930,16952],{"className":16929},[31],[28,16931,16933],{"className":16932},[35],[37,16934,16935],{"xmlns":39},[41,16936,16937,16949],{},[44,16938,16939,16941,16943,16945,16947],{},[47,16940,49],{},[51,16942,11216],{},[47,16944,7634],{},[51,16946,274],{},[47,16948,6642],{},[59,16950,16951],{"encoding":61},"R \\subseteq I+J",[28,16953,16955,16973,16991],{"className":16954,"ariaHidden":53},[66],[28,16956,16958,16961,16964,16967,16970],{"className":16957},[70],[28,16959],{"className":16960,"style":9234},[74],[28,16962,49],{"className":16963,"style":81},[79,80],[28,16965],{"className":16966,"style":140},[89],[28,16968,11216],{"className":16969},[144],[28,16971],{"className":16972,"style":140},[89],[28,16974,16976,16979,16982,16985,16988],{"className":16975},[70],[28,16977],{"className":16978,"style":10649},[74],[28,16980,7634],{"className":16981,"style":7654},[79,80],[28,16983],{"className":16984,"style":363},[89],[28,16986,274],{"className":16987},[367],[28,16989],{"className":16990,"style":363},[89],[28,16992,16994,16997],{"className":16993},[70],[28,16995],{"className":16996,"style":154},[74],[28,16998,6642],{"className":16999,"style":6663},[79,80],"，故 ",[28,17002,17004,17025],{"className":17003},[31],[28,17005,17007],{"className":17006},[35],[37,17008,17009],{"xmlns":39},[41,17010,17011,17023],{},[44,17012,17013,17015,17017,17019,17021],{},[47,17014,7634],{},[51,17016,274],{},[47,17018,6642],{},[51,17020,282],{},[47,17022,49],{},[59,17024,15661],{"encoding":61},[28,17026,17028,17046,17064],{"className":17027,"ariaHidden":53},[66],[28,17029,17031,17034,17037,17040,17043],{"className":17030},[70],[28,17032],{"className":17033,"style":10649},[74],[28,17035,7634],{"className":17036,"style":7654},[79,80],[28,17038],{"className":17039,"style":363},[89],[28,17041,274],{"className":17042},[367],[28,17044],{"className":17045,"style":363},[89],[28,17047,17049,17052,17055,17058,17061],{"className":17048},[70],[28,17050],{"className":17051,"style":154},[74],[28,17053,6642],{"className":17054,"style":6663},[79,80],[28,17056],{"className":17057,"style":140},[89],[28,17059,282],{"className":17060},[144],[28,17062],{"className":17063,"style":140},[89],[28,17065,17067,17070],{"className":17066},[70],[28,17068],{"className":17069,"style":154},[74],[28,17071,49],{"className":17072,"style":81},[79,80],", 即 ",[28,17075,17077,17094],{"className":17076},[31],[28,17078,17080],{"className":17079},[35],[37,17081,17082],{"xmlns":39},[41,17083,17084,17092],{},[44,17085,17086,17088,17090],{},[47,17087,7634],{},[51,17089,54],{"separator":53},[47,17091,6642],{},[59,17093,15731],{"encoding":61},[28,17095,17097],{"className":17096,"ariaHidden":53},[66],[28,17098,17100,17103,17106,17109,17112],{"className":17099},[70],[28,17101],{"className":17102,"style":75},[74],[28,17104,7634],{"className":17105,"style":7654},[79,80],[28,17107,54],{"className":17108},[85],[28,17110],{"className":17111,"style":90},[89],[28,17113,6642],{"className":17114,"style":6663},[79,80]," 互素。 ",[28,17117,17119,17132],{"className":17118},[31],[28,17120,17122],{"className":17121},[35],[37,17123,17124],{"xmlns":39},[41,17125,17126,17130],{},[44,17127,17128],{},[47,17129,6532],{"mathvariant":191},[59,17131,6535],{"encoding":61},[28,17133,17135],{"className":17134,"ariaHidden":53},[66],[28,17136,17138,17141],{"className":17137},[70],[28,17139],{"className":17140,"style":6545},[74],[28,17142,6532],{"className":17143},[79,2120],[20,17145,17146,17149,17150,17315,17316,17641],{},[23,17147,17148],{},"定义 3.3.3."," 由命题 3.2.5 知，两个理想的积也是理想。递归的可以定义有限个理想的积，设 ",[28,17151,17153,17188],{"className":17152},[31],[28,17154,17156],{"className":17155},[35],[37,17157,17158],{"xmlns":39},[41,17159,17160,17185],{},[44,17161,17162,17168,17170,17173,17175,17181,17183],{},[2621,17163,17164,17166],{},[47,17165,7634],{},[1731,17167,6706],{},[51,17169,54],{"separator":53},[51,17171,17172],{},"…",[51,17174,54],{"separator":53},[2621,17176,17177,17179],{},[47,17178,7634],{},[47,17180,11123],{},[51,17182,2090],{},[47,17184,49],{},[59,17186,17187],{"encoding":61},"I_1, \\dots, I_k \\lhd R",[28,17189,17191,17306],{"className":17190,"ariaHidden":53},[66],[28,17192,17194,17197,17237,17240,17243,17247,17250,17253,17256,17297,17300,17303],{"className":17193},[70],[28,17195],{"className":17196,"style":75},[74],[28,17198,17200,17203],{"className":17199},[79],[28,17201,7634],{"className":17202,"style":7654},[79,80],[28,17204,17206],{"className":17205},[2664],[28,17207,17209,17229],{"className":17208},[2668,2669],[28,17210,17212,17226],{"className":17211},[2673],[28,17213,17215],{"className":17214,"style":11486},[2677],[28,17216,17217,17220],{"style":15432},[28,17218],{"className":17219,"style":2686},[2685],[28,17221,17223],{"className":17222},[2690,2691,2692,2693],[28,17224,6706],{"className":17225},[79,2693],[28,17227,2701],{"className":17228},[2700],[28,17230,17232],{"className":17231},[2673],[28,17233,17235],{"className":17234,"style":2708},[2677],[28,17236],{},[28,17238,54],{"className":17239},[85],[28,17241],{"className":17242,"style":90},[89],[28,17244,17172],{"className":17245},[17246],"minner",[28,17248],{"className":17249,"style":90},[89],[28,17251,54],{"className":17252},[85],[28,17254],{"className":17255,"style":90},[89],[28,17257,17259,17262],{"className":17258},[79],[28,17260,7634],{"className":17261,"style":7654},[79,80],[28,17263,17265],{"className":17264},[2664],[28,17266,17268,17289],{"className":17267},[2668,2669],[28,17269,17271,17286],{"className":17270},[2673],[28,17272,17275],{"className":17273,"style":17274},[2677],"height:0.3361em;",[28,17276,17277,17280],{"style":15432},[28,17278],{"className":17279,"style":2686},[2685],[28,17281,17283],{"className":17282},[2690,2691,2692,2693],[28,17284,11123],{"className":17285,"style":11155},[79,80,2693],[28,17287,2701],{"className":17288},[2700],[28,17290,17292],{"className":17291},[2673],[28,17293,17295],{"className":17294,"style":2708},[2677],[28,17296],{},[28,17298],{"className":17299,"style":363},[89],[28,17301,2090],{"className":17302},[367,2120],[28,17304],{"className":17305,"style":363},[89],[28,17307,17309,17312],{"className":17308},[70],[28,17310],{"className":17311,"style":154},[74],[28,17313,49],{"className":17314,"style":81},[79,80],", 定义\n",[28,17317,17319,17380],{"className":17318},[31],[28,17320,17322],{"className":17321},[35],[37,17323,17324],{"xmlns":39},[41,17325,17326,17377],{},[44,17327,17328,17334,17337,17343,17345,17347,17353,17355,17367,17369,17375],{},[2621,17329,17330,17332],{},[47,17331,7634],{},[1731,17333,6706],{},[51,17335,17336],{},"⋯",[2621,17338,17339,17341],{},[47,17340,7634],{},[47,17342,11123],{},[51,17344,282],{},[51,17346,269],{"stretchy":268},[2621,17348,17349,17351],{},[47,17350,7634],{},[1731,17352,6706],{},[51,17354,17336],{},[2621,17356,17357,17359],{},[47,17358,7634],{},[44,17360,17361,17363,17365],{},[47,17362,11123],{},[51,17364,3201],{},[1731,17366,6706],{},[51,17368,279],{"stretchy":268},[2621,17370,17371,17373],{},[47,17372,7634],{},[47,17374,11123],{},[47,17376,336],{"mathvariant":191},[59,17378,17379],{"encoding":61},"I_1 \\cdots I_k = (I_1 \\cdots I_{k-1})I_k.",[28,17381,17383,17487],{"className":17382,"ariaHidden":53},[66],[28,17384,17386,17389,17429,17432,17435,17438,17478,17481,17484],{"className":17385},[70],[28,17387],{"className":17388,"style":15411},[74],[28,17390,17392,17395],{"className":17391},[79],[28,17393,7634],{"className":17394,"style":7654},[79,80],[28,17396,17398],{"className":17397},[2664],[28,17399,17401,17421],{"className":17400},[2668,2669],[28,17402,17404,17418],{"className":17403},[2673],[28,17405,17407],{"className":17406,"style":11486},[2677],[28,17408,17409,17412],{"style":15432},[28,17410],{"className":17411,"style":2686},[2685],[28,17413,17415],{"className":17414},[2690,2691,2692,2693],[28,17416,6706],{"className":17417},[79,2693],[28,17419,2701],{"className":17420},[2700],[28,17422,17424],{"className":17423},[2673],[28,17425,17427],{"className":17426,"style":2708},[2677],[28,17428],{},[28,17430],{"className":17431,"style":90},[89],[28,17433,17336],{"className":17434},[17246],[28,17436],{"className":17437,"style":90},[89],[28,17439,17441,17444],{"className":17440},[79],[28,17442,7634],{"className":17443,"style":7654},[79,80],[28,17445,17447],{"className":17446},[2664],[28,17448,17450,17470],{"className":17449},[2668,2669],[28,17451,17453,17467],{"className":17452},[2673],[28,17454,17456],{"className":17455,"style":17274},[2677],[28,17457,17458,17461],{"style":15432},[28,17459],{"className":17460,"style":2686},[2685],[28,17462,17464],{"className":17463},[2690,2691,2692,2693],[28,17465,11123],{"className":17466,"style":11155},[79,80,2693],[28,17468,2701],{"className":17469},[2700],[28,17471,17473],{"className":17472},[2673],[28,17474,17476],{"className":17475,"style":2708},[2677],[28,17477],{},[28,17479],{"className":17480,"style":140},[89],[28,17482,282],{"className":17483},[144],[28,17485],{"className":17486,"style":140},[89],[28,17488,17490,17493,17496,17536,17539,17542,17545,17595,17598,17638],{"className":17489},[70],[28,17491],{"className":17492,"style":349},[74],[28,17494,269],{"className":17495},[356],[28,17497,17499,17502],{"className":17498},[79],[28,17500,7634],{"className":17501,"style":7654},[79,80],[28,17503,17505],{"className":17504},[2664],[28,17506,17508,17528],{"className":17507},[2668,2669],[28,17509,17511,17525],{"className":17510},[2673],[28,17512,17514],{"className":17513,"style":11486},[2677],[28,17515,17516,17519],{"style":15432},[28,17517],{"className":17518,"style":2686},[2685],[28,17520,17522],{"className":17521},[2690,2691,2692,2693],[28,17523,6706],{"className":17524},[79,2693],[28,17526,2701],{"className":17527},[2700],[28,17529,17531],{"className":17530},[2673],[28,17532,17534],{"className":17533,"style":2708},[2677],[28,17535],{},[28,17537],{"className":17538,"style":90},[89],[28,17540,17336],{"className":17541},[17246],[28,17543],{"className":17544,"style":90},[89],[28,17546,17548,17551],{"className":17547},[79],[28,17549,7634],{"className":17550,"style":7654},[79,80],[28,17552,17554],{"className":17553},[2664],[28,17555,17557,17586],{"className":17556},[2668,2669],[28,17558,17560,17583],{"className":17559},[2673],[28,17561,17563],{"className":17562,"style":17274},[2677],[28,17564,17565,17568],{"style":15432},[28,17566],{"className":17567,"style":2686},[2685],[28,17569,17571],{"className":17570},[2690,2691,2692,2693],[28,17572,17574,17577,17580],{"className":17573},[79,2693],[28,17575,11123],{"className":17576,"style":11155},[79,80,2693],[28,17578,3201],{"className":17579},[367,2693],[28,17581,6706],{"className":17582},[79,2693],[28,17584,2701],{"className":17585},[2700],[28,17587,17589],{"className":17588},[2673],[28,17590,17593],{"className":17591,"style":17592},[2677],"height:0.2083em;",[28,17594],{},[28,17596,279],{"className":17597},[383],[28,17599,17601,17604],{"className":17600},[79],[28,17602,7634],{"className":17603,"style":7654},[79,80],[28,17605,17607],{"className":17606},[2664],[28,17608,17610,17630],{"className":17609},[2668,2669],[28,17611,17613,17627],{"className":17612},[2673],[28,17614,17616],{"className":17615,"style":17274},[2677],[28,17617,17618,17621],{"style":15432},[28,17619],{"className":17620,"style":2686},[2685],[28,17622,17624],{"className":17623},[2690,2691,2692,2693],[28,17625,11123],{"className":17626,"style":11155},[79,80,2693],[28,17628,2701],{"className":17629},[2700],[28,17631,17633],{"className":17632},[2673],[28,17634,17636],{"className":17635,"style":2708},[2677],[28,17637],{},[28,17639,336],{"className":17640},[79],[9797,17642,17643,17644,17678,17679,17807,17808,17977],{},"(注：理想的积 ",[28,17645,17647,17663],{"className":17646},[31],[28,17648,17650],{"className":17649},[35],[37,17651,17652],{"xmlns":39},[41,17653,17654,17660],{},[44,17655,17656,17658],{},[47,17657,7634],{},[47,17659,6642],{},[59,17661,17662],{"encoding":61},"IJ",[28,17664,17666],{"className":17665,"ariaHidden":53},[66],[28,17667,17669,17672,17675],{"className":17668},[70],[28,17670],{"className":17671,"style":154},[74],[28,17673,7634],{"className":17674,"style":7654},[79,80],[28,17676,6642],{"className":17677,"style":6663},[79,80]," 是由所有形式为 ",[28,17680,17682,17709],{"className":17681},[31],[28,17683,17685],{"className":17684},[35],[37,17686,17687],{"xmlns":39},[41,17688,17689,17706],{},[44,17690,17691,17694,17700],{},[51,17692,17693],{},"∑",[2621,17695,17696,17698],{},[47,17697,195],{},[47,17699,11123],{},[2621,17701,17702,17704],{},[47,17703,200],{},[47,17705,11123],{},[59,17707,17708],{"encoding":61},"\\sum a_k b_k",[28,17710,17712],{"className":17711,"ariaHidden":53},[66],[28,17713,17715,17718,17724,17727,17767],{"className":17714},[70],[28,17716],{"className":17717,"style":349},[74],[28,17719,17693],{"className":17720,"style":17723},[1385,17721,17722],"op-symbol","small-op","position:relative;top:0em;",[28,17725],{"className":17726,"style":90},[89],[28,17728,17730,17733],{"className":17729},[79],[28,17731,195],{"className":17732},[79,80],[28,17734,17736],{"className":17735},[2664],[28,17737,17739,17759],{"className":17738},[2668,2669],[28,17740,17742,17756],{"className":17741},[2673],[28,17743,17745],{"className":17744,"style":17274},[2677],[28,17746,17747,17750],{"style":2681},[28,17748],{"className":17749,"style":2686},[2685],[28,17751,17753],{"className":17752},[2690,2691,2692,2693],[28,17754,11123],{"className":17755,"style":11155},[79,80,2693],[28,17757,2701],{"className":17758},[2700],[28,17760,17762],{"className":17761},[2673],[28,17763,17765],{"className":17764,"style":2708},[2677],[28,17766],{},[28,17768,17770,17773],{"className":17769},[79],[28,17771,200],{"className":17772},[79,80],[28,17774,17776],{"className":17775},[2664],[28,17777,17779,17799],{"className":17778},[2668,2669],[28,17780,17782,17796],{"className":17781},[2673],[28,17783,17785],{"className":17784,"style":17274},[2677],[28,17786,17787,17790],{"style":2681},[28,17788],{"className":17789,"style":2686},[2685],[28,17791,17793],{"className":17792},[2690,2691,2692,2693],[28,17794,11123],{"className":17795,"style":11155},[79,80,2693],[28,17797,2701],{"className":17798},[2700],[28,17800,17802],{"className":17801},[2673],[28,17803,17805],{"className":17804,"style":2708},[2677],[28,17806],{}," (",[28,17809,17811,17845],{"className":17810},[31],[28,17812,17814],{"className":17813},[35],[37,17815,17816],{"xmlns":39},[41,17817,17818,17842],{},[44,17819,17820,17826,17828,17830,17832,17838,17840],{},[2621,17821,17822,17824],{},[47,17823,195],{},[47,17825,11123],{},[51,17827,203],{},[47,17829,7634],{},[51,17831,54],{"separator":53},[2621,17833,17834,17836],{},[47,17835,200],{},[47,17837,11123],{},[51,17839,203],{},[47,17841,6642],{},[59,17843,17844],{"encoding":61},"a_k \\in I, b_k \\in J",[28,17846,17848,17904,17968],{"className":17847,"ariaHidden":53},[66],[28,17849,17851,17855,17895,17898,17901],{"className":17850},[70],[28,17852],{"className":17853,"style":17854},[74],"height:0.6891em;vertical-align:-0.15em;",[28,17856,17858,17861],{"className":17857},[79],[28,17859,195],{"className":17860},[79,80],[28,17862,17864],{"className":17863},[2664],[28,17865,17867,17887],{"className":17866},[2668,2669],[28,17868,17870,17884],{"className":17869},[2673],[28,17871,17873],{"className":17872,"style":17274},[2677],[28,17874,17875,17878],{"style":2681},[28,17876],{"className":17877,"style":2686},[2685],[28,17879,17881],{"className":17880},[2690,2691,2692,2693],[28,17882,11123],{"className":17883,"style":11155},[79,80,2693],[28,17885,2701],{"className":17886},[2700],[28,17888,17890],{"className":17889},[2673],[28,17891,17893],{"className":17892,"style":2708},[2677],[28,17894],{},[28,17896],{"className":17897,"style":140},[89],[28,17899,203],{"className":17900},[144],[28,17902],{"className":17903,"style":140},[89],[28,17905,17907,17910,17913,17916,17919,17959,17962,17965],{"className":17906},[70],[28,17908],{"className":17909,"style":133},[74],[28,17911,7634],{"className":17912,"style":7654},[79,80],[28,17914,54],{"className":17915},[85],[28,17917],{"className":17918,"style":90},[89],[28,17920,17922,17925],{"className":17921},[79],[28,17923,200],{"className":17924},[79,80],[28,17926,17928],{"className":17927},[2664],[28,17929,17931,17951],{"className":17930},[2668,2669],[28,17932,17934,17948],{"className":17933},[2673],[28,17935,17937],{"className":17936,"style":17274},[2677],[28,17938,17939,17942],{"style":2681},[28,17940],{"className":17941,"style":2686},[2685],[28,17943,17945],{"className":17944},[2690,2691,2692,2693],[28,17946,11123],{"className":17947,"style":11155},[79,80,2693],[28,17949,2701],{"className":17950},[2700],[28,17952,17954],{"className":17953},[2673],[28,17955,17957],{"className":17956,"style":2708},[2677],[28,17958],{},[28,17960],{"className":17961,"style":140},[89],[28,17963,203],{"className":17964},[144],[28,17966],{"className":17967,"style":140},[89],[28,17969,17971,17974],{"className":17970},[70],[28,17972],{"className":17973,"style":154},[74],[28,17975,6642],{"className":17976,"style":6663},[79,80],") 的有限和构成的集合，而不仅仅是元素乘积的集合。)",[20,17979,17980,26,17983,18011,18012,18075,18076,18117,18118,6907,18223,18225,18226,18304,18305,18117,18346,18418,18419,949,18504,6907,18576,18654,18655,18846,18847,18963,18964,19106,19107,19168,19169,19279,19280,19358,19359,14342,19437],{},[23,17981,17982],{},"命题 3.3.4.",[28,17984,17986,17999],{"className":17985},[31],[28,17987,17989],{"className":17988},[35],[37,17990,17991],{"xmlns":39},[41,17992,17993,17997],{},[44,17994,17995],{},[47,17996,49],{},[59,17998,49],{"encoding":61},[28,18000,18002],{"className":18001,"ariaHidden":53},[66],[28,18003,18005,18008],{"className":18004},[70],[28,18006],{"className":18007,"style":154},[74],[28,18009,49],{"className":18010,"style":81},[79,80]," 是交换幺环, ",[28,18013,18015,18036],{"className":18014},[31],[28,18016,18018],{"className":18017},[35],[37,18019,18020],{"xmlns":39},[41,18021,18022,18034],{},[44,18023,18024,18026,18028,18030,18032],{},[47,18025,7634],{},[51,18027,54],{"separator":53},[47,18029,6642],{},[51,18031,2090],{},[47,18033,49],{},[59,18035,15596],{"encoding":61},[28,18037,18039,18066],{"className":18038,"ariaHidden":53},[66],[28,18040,18042,18045,18048,18051,18054,18057,18060,18063],{"className":18041},[70],[28,18043],{"className":18044,"style":75},[74],[28,18046,7634],{"className":18047,"style":7654},[79,80],[28,18049,54],{"className":18050},[85],[28,18052],{"className":18053,"style":90},[89],[28,18055,6642],{"className":18056,"style":6663},[79,80],[28,18058],{"className":18059,"style":363},[89],[28,18061,2090],{"className":18062},[367,2120],[28,18064],{"className":18065,"style":363},[89],[28,18067,18069,18072],{"className":18068},[70],[28,18070],{"className":18071,"style":154},[74],[28,18073,49],{"className":18074,"style":81},[79,80],". 若 ",[28,18077,18079,18096],{"className":18078},[31],[28,18080,18082],{"className":18081},[35],[37,18083,18084],{"xmlns":39},[41,18085,18086,18094],{},[44,18087,18088,18090,18092],{},[47,18089,7634],{},[51,18091,54],{"separator":53},[47,18093,6642],{},[59,18095,15731],{"encoding":61},[28,18097,18099],{"className":18098,"ariaHidden":53},[66],[28,18100,18102,18105,18108,18111,18114],{"className":18101},[70],[28,18103],{"className":18104,"style":75},[74],[28,18106,7634],{"className":18107,"style":7654},[79,80],[28,18109,54],{"className":18110},[85],[28,18112],{"className":18113,"style":90},[89],[28,18115,6642],{"className":18116,"style":6663},[79,80]," 互素，则 ",[28,18119,18121,18151],{"className":18120},[31],[28,18122,18124],{"className":18123},[35],[37,18125,18126],{"xmlns":39},[41,18127,18128,18148],{},[44,18129,18130,18132,18134,18136,18138,18140,18142,18144,18146],{},[47,18131,7634],{},[47,18133,6642],{},[51,18135,282],{},[47,18137,7634],{},[51,18139,10630],{},[47,18141,6642],{},[51,18143,282],{},[47,18145,6642],{},[47,18147,7634],{},[59,18149,18150],{"encoding":61},"IJ = I \\cap J = JI",[28,18152,18154,18175,18193,18211],{"className":18153,"ariaHidden":53},[66],[28,18155,18157,18160,18163,18166,18169,18172],{"className":18156},[70],[28,18158],{"className":18159,"style":154},[74],[28,18161,7634],{"className":18162,"style":7654},[79,80],[28,18164,6642],{"className":18165,"style":6663},[79,80],[28,18167],{"className":18168,"style":140},[89],[28,18170,282],{"className":18171},[144],[28,18173],{"className":18174,"style":140},[89],[28,18176,18178,18181,18184,18187,18190],{"className":18177},[70],[28,18179],{"className":18180,"style":154},[74],[28,18182,7634],{"className":18183,"style":7654},[79,80],[28,18185],{"className":18186,"style":363},[89],[28,18188,10630],{"className":18189},[367],[28,18191],{"className":18192,"style":363},[89],[28,18194,18196,18199,18202,18205,18208],{"className":18195},[70],[28,18197],{"className":18198,"style":154},[74],[28,18200,6642],{"className":18201,"style":6663},[79,80],[28,18203],{"className":18204,"style":140},[89],[28,18206,282],{"className":18207},[144],[28,18209],{"className":18210,"style":140},[89],[28,18212,18214,18217,18220],{"className":18213},[70],[28,18215],{"className":18216,"style":154},[74],[28,18218,6642],{"className":18219,"style":6663},[79,80],[28,18221,7634],{"className":18222,"style":7654},[79,80],[23,18224,6910],{},"\n一方面，显然有 ",[28,18227,18229,18253],{"className":18228},[31],[28,18230,18232],{"className":18231},[35],[37,18233,18234],{"xmlns":39},[41,18235,18236,18250],{},[44,18237,18238,18240,18242,18244,18246,18248],{},[47,18239,7634],{},[47,18241,6642],{},[51,18243,11216],{},[47,18245,7634],{},[51,18247,10630],{},[47,18249,6642],{},[59,18251,18252],{"encoding":61},"IJ \\subseteq I \\cap J",[28,18254,18256,18277,18295],{"className":18255,"ariaHidden":53},[66],[28,18257,18259,18262,18265,18268,18271,18274],{"className":18258},[70],[28,18260],{"className":18261,"style":9234},[74],[28,18263,7634],{"className":18264,"style":7654},[79,80],[28,18266,6642],{"className":18267,"style":6663},[79,80],[28,18269],{"className":18270,"style":140},[89],[28,18272,11216],{"className":18273},[144],[28,18275],{"className":18276,"style":140},[89],[28,18278,18280,18283,18286,18289,18292],{"className":18279},[70],[28,18281],{"className":18282,"style":154},[74],[28,18284,7634],{"className":18285,"style":7654},[79,80],[28,18287],{"className":18288,"style":363},[89],[28,18290,10630],{"className":18291},[367],[28,18293],{"className":18294,"style":363},[89],[28,18296,18298,18301],{"className":18297},[70],[28,18299],{"className":18300,"style":154},[74],[28,18302,6642],{"className":18303,"style":6663},[79,80],"（这是理想积的一般性质）。\n反过来，如果 ",[28,18306,18308,18325],{"className":18307},[31],[28,18309,18311],{"className":18310},[35],[37,18312,18313],{"xmlns":39},[41,18314,18315,18323],{},[44,18316,18317,18319,18321],{},[47,18318,7634],{},[51,18320,54],{"separator":53},[47,18322,6642],{},[59,18324,15731],{"encoding":61},[28,18326,18328],{"className":18327,"ariaHidden":53},[66],[28,18329,18331,18334,18337,18340,18343],{"className":18330},[70],[28,18332],{"className":18333,"style":75},[74],[28,18335,7634],{"className":18336,"style":7654},[79,80],[28,18338,54],{"className":18339},[85],[28,18341],{"className":18342,"style":90},[89],[28,18344,6642],{"className":18345,"style":6663},[79,80],[28,18347,18349,18370],{"className":18348},[31],[28,18350,18352],{"className":18351},[35],[37,18353,18354],{"xmlns":39},[41,18355,18356,18368],{},[44,18357,18358,18360,18362,18364,18366],{},[47,18359,7634],{},[51,18361,274],{},[47,18363,6642],{},[51,18365,282],{},[47,18367,49],{},[59,18369,15661],{"encoding":61},[28,18371,18373,18391,18409],{"className":18372,"ariaHidden":53},[66],[28,18374,18376,18379,18382,18385,18388],{"className":18375},[70],[28,18377],{"className":18378,"style":10649},[74],[28,18380,7634],{"className":18381,"style":7654},[79,80],[28,18383],{"className":18384,"style":363},[89],[28,18386,274],{"className":18387},[367],[28,18389],{"className":18390,"style":363},[89],[28,18392,18394,18397,18400,18403,18406],{"className":18393},[70],[28,18395],{"className":18396,"style":154},[74],[28,18398,6642],{"className":18399,"style":6663},[79,80],[28,18401],{"className":18402,"style":140},[89],[28,18404,282],{"className":18405},[144],[28,18407],{"className":18408,"style":140},[89],[28,18410,18412,18415],{"className":18411},[70],[28,18413],{"className":18414,"style":154},[74],[28,18416,49],{"className":18417,"style":81},[79,80],". 由命题 3.3.3，存在 ",[28,18420,18422,18447],{"className":18421},[31],[28,18423,18425],{"className":18424},[35],[37,18426,18427],{"xmlns":39},[41,18428,18429,18445],{},[44,18430,18431,18433,18435,18437,18439,18441,18443],{},[47,18432,12938],{},[51,18434,203],{},[47,18436,7634],{},[51,18438,54],{"separator":53},[47,18440,15917],{},[51,18442,203],{},[47,18444,6642],{},[59,18446,15924],{"encoding":61},[28,18448,18450,18468,18495],{"className":18449,"ariaHidden":53},[66],[28,18451,18453,18456,18459,18462,18465],{"className":18452},[70],[28,18454],{"className":18455,"style":13045},[74],[28,18457,12938],{"className":18458},[79,80],[28,18460],{"className":18461,"style":140},[89],[28,18463,203],{"className":18464},[144],[28,18466],{"className":18467,"style":140},[89],[28,18469,18471,18474,18477,18480,18483,18486,18489,18492],{"className":18470},[70],[28,18472],{"className":18473,"style":75},[74],[28,18475,7634],{"className":18476,"style":7654},[79,80],[28,18478,54],{"className":18479},[85],[28,18481],{"className":18482,"style":90},[89],[28,18484,15917],{"className":18485,"style":15964},[79,80],[28,18487],{"className":18488,"style":140},[89],[28,18490,203],{"className":18491},[144],[28,18493],{"className":18494,"style":140},[89],[28,18496,18498,18501],{"className":18497},[70],[28,18499],{"className":18500,"style":154},[74],[28,18502,6642],{"className":18503,"style":6663},[79,80],[28,18505,18507,18528],{"className":18506},[31],[28,18508,18510],{"className":18509},[35],[37,18511,18512],{"xmlns":39},[41,18513,18514,18526],{},[44,18515,18516,18518,18520,18522,18524],{},[1731,18517,6706],{},[51,18519,282],{},[47,18521,12938],{},[51,18523,274],{},[47,18525,15917],{},[59,18527,16008],{"encoding":61},[28,18529,18531,18549,18567],{"className":18530,"ariaHidden":53},[66],[28,18532,18534,18537,18540,18543,18546],{"className":18533},[70],[28,18535],{"className":18536,"style":3176},[74],[28,18538,6706],{"className":18539},[79],[28,18541],{"className":18542,"style":140},[89],[28,18544,282],{"className":18545},[144],[28,18547],{"className":18548,"style":140},[89],[28,18550,18552,18555,18558,18561,18564],{"className":18551},[70],[28,18553],{"className":18554,"style":16036},[74],[28,18556,12938],{"className":18557},[79,80],[28,18559],{"className":18560,"style":363},[89],[28,18562,274],{"className":18563},[367],[28,18565],{"className":18566,"style":363},[89],[28,18568,18570,18573],{"className":18569},[70],[28,18571],{"className":18572,"style":16055},[74],[28,18574,15917],{"className":18575,"style":15964},[79,80],[28,18577,18579,18603],{"className":18578},[31],[28,18580,18582],{"className":18581},[35],[37,18583,18584],{"xmlns":39},[41,18585,18586,18600],{},[44,18587,18588,18590,18592,18594,18596,18598],{},[47,18589,192],{"mathvariant":191},[47,18591,4430],{},[51,18593,203],{},[47,18595,7634],{},[51,18597,10630],{},[47,18599,6642],{},[59,18601,18602],{"encoding":61},"\\forall x \\in I \\cap J",[28,18604,18606,18627,18645],{"className":18605,"ariaHidden":53},[66],[28,18607,18609,18612,18615,18618,18621,18624],{"className":18608},[70],[28,18610],{"className":18611,"style":893},[74],[28,18613,192],{"className":18614},[79],[28,18616,4430],{"className":18617},[79,80],[28,18619],{"className":18620,"style":140},[89],[28,18622,203],{"className":18623},[144],[28,18625],{"className":18626,"style":140},[89],[28,18628,18630,18633,18636,18639,18642],{"className":18629},[70],[28,18631],{"className":18632,"style":154},[74],[28,18634,7634],{"className":18635,"style":7654},[79,80],[28,18637],{"className":18638,"style":363},[89],[28,18640,10630],{"className":18641},[367],[28,18643],{"className":18644,"style":363},[89],[28,18646,18648,18651],{"className":18647},[70],[28,18649],{"className":18650,"style":154},[74],[28,18652,6642],{"className":18653,"style":6663},[79,80],", 有\n",[28,18656,18658,18708],{"className":18657},[31],[28,18659,18661],{"className":18660},[35],[37,18662,18663],{"xmlns":39},[41,18664,18665,18705],{},[44,18666,18667,18669,18671,18673,18675,18677,18679,18681,18683,18685,18687,18689,18691,18693,18695,18697,18699,18701,18703],{},[47,18668,4430],{},[51,18670,282],{},[1731,18672,6706],{},[51,18674,3732],{},[47,18676,4430],{},[51,18678,282],{},[51,18680,269],{"stretchy":268},[47,18682,12938],{},[51,18684,274],{},[47,18686,15917],{},[51,18688,279],{"stretchy":268},[47,18690,4430],{},[51,18692,282],{},[47,18694,12938],{},[47,18696,4430],{},[51,18698,274],{},[47,18700,15917],{},[47,18702,4430],{},[47,18704,336],{"mathvariant":191},[59,18706,18707],{"encoding":61},"x = 1 \\cdot x = (i+j)x = ix + jx.",[28,18709,18711,18729,18747,18765,18786,18810,18831],{"className":18710,"ariaHidden":53},[66],[28,18712,18714,18717,18720,18723,18726],{"className":18713},[70],[28,18715],{"className":18716,"style":761},[74],[28,18718,4430],{"className":18719},[79,80],[28,18721],{"className":18722,"style":140},[89],[28,18724,282],{"className":18725},[144],[28,18727],{"className":18728,"style":140},[89],[28,18730,18732,18735,18738,18741,18744],{"className":18731},[70],[28,18733],{"className":18734,"style":3176},[74],[28,18736,6706],{"className":18737},[79],[28,18739],{"className":18740,"style":363},[89],[28,18742,3732],{"className":18743},[367],[28,18745],{"className":18746,"style":363},[89],[28,18748,18750,18753,18756,18759,18762],{"className":18749},[70],[28,18751],{"className":18752,"style":761},[74],[28,18754,4430],{"className":18755},[79,80],[28,18757],{"className":18758,"style":140},[89],[28,18760,282],{"className":18761},[144],[28,18763],{"className":18764,"style":140},[89],[28,18766,18768,18771,18774,18777,18780,18783],{"className":18767},[70],[28,18769],{"className":18770,"style":349},[74],[28,18772,269],{"className":18773},[356],[28,18775,12938],{"className":18776},[79,80],[28,18778],{"className":18779,"style":363},[89],[28,18781,274],{"className":18782},[367],[28,18784],{"className":18785,"style":363},[89],[28,18787,18789,18792,18795,18798,18801,18804,18807],{"className":18788},[70],[28,18790],{"className":18791,"style":349},[74],[28,18793,15917],{"className":18794,"style":15964},[79,80],[28,18796,279],{"className":18797},[383],[28,18799,4430],{"className":18800},[79,80],[28,18802],{"className":18803,"style":140},[89],[28,18805,282],{"className":18806},[144],[28,18808],{"className":18809,"style":140},[89],[28,18811,18813,18816,18819,18822,18825,18828],{"className":18812},[70],[28,18814],{"className":18815,"style":16036},[74],[28,18817,12938],{"className":18818},[79,80],[28,18820,4430],{"className":18821},[79,80],[28,18823],{"className":18824,"style":363},[89],[28,18826,274],{"className":18827},[367],[28,18829],{"className":18830,"style":363},[89],[28,18832,18834,18837,18840,18843],{"className":18833},[70],[28,18835],{"className":18836,"style":16055},[74],[28,18838,15917],{"className":18839,"style":15964},[79,80],[28,18841,4430],{"className":18842},[79,80],[28,18844,336],{"className":18845},[79],"\n因为 ",[28,18848,18850,18884],{"className":18849},[31],[28,18851,18853],{"className":18852},[35],[37,18854,18855],{"xmlns":39},[41,18856,18857,18881],{},[44,18858,18859,18861,18863,18865,18867,18869,18871,18873,18875,18877,18879],{},[47,18860,4430],{},[51,18862,203],{},[47,18864,6642],{},[3239,18866,3241],{},[51,18868,3244],{},[3239,18870,3241],{},[47,18872,12938],{},[47,18874,4430],{},[51,18876,203],{},[47,18878,7634],{},[47,18880,6642],{},[59,18882,18883],{"encoding":61},"x \\in J \\implies ix \\in IJ",[28,18885,18887,18905,18930,18951],{"className":18886,"ariaHidden":53},[66],[28,18888,18890,18893,18896,18899,18902],{"className":18889},[70],[28,18891],{"className":18892,"style":1960},[74],[28,18894,4430],{"className":18895},[79,80],[28,18897],{"className":18898,"style":140},[89],[28,18900,203],{"className":18901},[144],[28,18903],{"className":18904,"style":140},[89],[28,18906,18908,18912,18915,18918,18921,18924,18927],{"className":18907},[70],[28,18909],{"className":18910,"style":18911},[74],"height:0.7073em;vertical-align:-0.024em;",[28,18913,6642],{"className":18914,"style":6663},[79,80],[28,18916],{"className":18917,"style":140},[89],[28,18919],{"className":18920,"style":140},[89],[28,18922,3244],{"className":18923},[144],[28,18925],{"className":18926,"style":140},[89],[28,18928],{"className":18929,"style":140},[89],[28,18931,18933,18936,18939,18942,18945,18948],{"className":18932},[70],[28,18934],{"className":18935,"style":13045},[74],[28,18937,12938],{"className":18938},[79,80],[28,18940,4430],{"className":18941},[79,80],[28,18943],{"className":18944,"style":140},[89],[28,18946,203],{"className":18947},[144],[28,18949],{"className":18950,"style":140},[89],[28,18952,18954,18957,18960],{"className":18953},[70],[28,18955],{"className":18956,"style":154},[74],[28,18958,7634],{"className":18959,"style":7654},[79,80],[28,18961,6642],{"className":18962,"style":6663},[79,80]," (理想性质)，且 ",[28,18965,18967,19007],{"className":18966},[31],[28,18968,18970],{"className":18969},[35],[37,18971,18972],{"xmlns":39},[41,18973,18974,19004],{},[44,18975,18976,18978,18980,18982,18984,18986,18988,18990,18992,18994,18996,18998,19000,19002],{},[47,18977,4430],{},[51,18979,203],{},[47,18981,7634],{},[3239,18983,3241],{},[51,18985,3244],{},[3239,18987,3241],{},[47,18989,15917],{},[47,18991,4430],{},[51,18993,203],{},[47,18995,6642],{},[47,18997,7634],{},[51,18999,282],{},[47,19001,7634],{},[47,19003,6642],{},[59,19005,19006],{"encoding":61},"x \\in I \\implies jx \\in JI = IJ",[28,19008,19010,19028,19052,19073,19094],{"className":19009,"ariaHidden":53},[66],[28,19011,19013,19016,19019,19022,19025],{"className":19012},[70],[28,19014],{"className":19015,"style":1960},[74],[28,19017,4430],{"className":19018},[79,80],[28,19020],{"className":19021,"style":140},[89],[28,19023,203],{"className":19024},[144],[28,19026],{"className":19027,"style":140},[89],[28,19029,19031,19034,19037,19040,19043,19046,19049],{"className":19030},[70],[28,19032],{"className":19033,"style":18911},[74],[28,19035,7634],{"className":19036,"style":7654},[79,80],[28,19038],{"className":19039,"style":140},[89],[28,19041],{"className":19042,"style":140},[89],[28,19044,3244],{"className":19045},[144],[28,19047],{"className":19048,"style":140},[89],[28,19050],{"className":19051,"style":140},[89],[28,19053,19055,19058,19061,19064,19067,19070],{"className":19054},[70],[28,19056],{"className":19057,"style":16055},[74],[28,19059,15917],{"className":19060,"style":15964},[79,80],[28,19062,4430],{"className":19063},[79,80],[28,19065],{"className":19066,"style":140},[89],[28,19068,203],{"className":19069},[144],[28,19071],{"className":19072,"style":140},[89],[28,19074,19076,19079,19082,19085,19088,19091],{"className":19075},[70],[28,19077],{"className":19078,"style":154},[74],[28,19080,6642],{"className":19081,"style":6663},[79,80],[28,19083,7634],{"className":19084,"style":7654},[79,80],[28,19086],{"className":19087,"style":140},[89],[28,19089,282],{"className":19090},[144],[28,19092],{"className":19093,"style":140},[89],[28,19095,19097,19100,19103],{"className":19096},[70],[28,19098],{"className":19099,"style":154},[74],[28,19101,7634],{"className":19102,"style":7654},[79,80],[28,19104,6642],{"className":19105,"style":6663},[79,80]," (交换环中 ",[28,19108,19110,19132],{"className":19109},[31],[28,19111,19113],{"className":19112},[35],[37,19114,19115],{"xmlns":39},[41,19116,19117,19129],{},[44,19118,19119,19121,19123,19125,19127],{},[47,19120,6642],{},[47,19122,7634],{},[51,19124,282],{},[47,19126,7634],{},[47,19128,6642],{},[59,19130,19131],{"encoding":61},"JI=IJ",[28,19133,19135,19156],{"className":19134,"ariaHidden":53},[66],[28,19136,19138,19141,19144,19147,19150,19153],{"className":19137},[70],[28,19139],{"className":19140,"style":154},[74],[28,19142,6642],{"className":19143,"style":6663},[79,80],[28,19145,7634],{"className":19146,"style":7654},[79,80],[28,19148],{"className":19149,"style":140},[89],[28,19151,282],{"className":19152},[144],[28,19154],{"className":19155,"style":140},[89],[28,19157,19159,19162,19165],{"className":19158},[70],[28,19160],{"className":19161,"style":154},[74],[28,19163,7634],{"className":19164,"style":7654},[79,80],[28,19166,6642],{"className":19167,"style":6663},[79,80],")。\n所以 ",[28,19170,19172,19204],{"className":19171},[31],[28,19173,19175],{"className":19174},[35],[37,19176,19177],{"xmlns":39},[41,19178,19179,19201],{},[44,19180,19181,19183,19185,19187,19189,19191,19193,19195,19197,19199],{},[47,19182,4430],{},[51,19184,203],{},[47,19186,7634],{},[47,19188,6642],{},[51,19190,274],{},[47,19192,7634],{},[47,19194,6642],{},[51,19196,282],{},[47,19198,7634],{},[47,19200,6642],{},[59,19202,19203],{"encoding":61},"x \\in IJ + IJ = IJ",[28,19205,19207,19225,19246,19267],{"className":19206,"ariaHidden":53},[66],[28,19208,19210,19213,19216,19219,19222],{"className":19209},[70],[28,19211],{"className":19212,"style":1960},[74],[28,19214,4430],{"className":19215},[79,80],[28,19217],{"className":19218,"style":140},[89],[28,19220,203],{"className":19221},[144],[28,19223],{"className":19224,"style":140},[89],[28,19226,19228,19231,19234,19237,19240,19243],{"className":19227},[70],[28,19229],{"className":19230,"style":10649},[74],[28,19232,7634],{"className":19233,"style":7654},[79,80],[28,19235,6642],{"className":19236,"style":6663},[79,80],[28,19238],{"className":19239,"style":363},[89],[28,19241,274],{"className":19242},[367],[28,19244],{"className":19245,"style":363},[89],[28,19247,19249,19252,19255,19258,19261,19264],{"className":19248},[70],[28,19250],{"className":19251,"style":154},[74],[28,19253,7634],{"className":19254,"style":7654},[79,80],[28,19256,6642],{"className":19257,"style":6663},[79,80],[28,19259],{"className":19260,"style":140},[89],[28,19262,282],{"className":19263},[144],[28,19265],{"className":19266,"style":140},[89],[28,19268,19270,19273,19276],{"className":19269},[70],[28,19271],{"className":19272,"style":154},[74],[28,19274,7634],{"className":19275,"style":7654},[79,80],[28,19277,6642],{"className":19278,"style":6663},[79,80],"。\n因此 ",[28,19281,19283,19307],{"className":19282},[31],[28,19284,19286],{"className":19285},[35],[37,19287,19288],{"xmlns":39},[41,19289,19290,19304],{},[44,19291,19292,19294,19296,19298,19300,19302],{},[47,19293,7634],{},[51,19295,10630],{},[47,19297,6642],{},[51,19299,11216],{},[47,19301,7634],{},[47,19303,6642],{},[59,19305,19306],{"encoding":61},"I \\cap J \\subseteq IJ",[28,19308,19310,19328,19346],{"className":19309,"ariaHidden":53},[66],[28,19311,19313,19316,19319,19322,19325],{"className":19312},[70],[28,19314],{"className":19315,"style":154},[74],[28,19317,7634],{"className":19318,"style":7654},[79,80],[28,19320],{"className":19321,"style":363},[89],[28,19323,10630],{"className":19324},[367],[28,19326],{"className":19327,"style":363},[89],[28,19329,19331,19334,19337,19340,19343],{"className":19330},[70],[28,19332],{"className":19333,"style":9234},[74],[28,19335,6642],{"className":19336,"style":6663},[79,80],[28,19338],{"className":19339,"style":140},[89],[28,19341,11216],{"className":19342},[144],[28,19344],{"className":19345,"style":140},[89],[28,19347,19349,19352,19355],{"className":19348},[70],[28,19350],{"className":19351,"style":154},[74],[28,19353,7634],{"className":19354,"style":7654},[79,80],[28,19356,6642],{"className":19357,"style":6663},[79,80],". 综上 ",[28,19360,19362,19386],{"className":19361},[31],[28,19363,19365],{"className":19364},[35],[37,19366,19367],{"xmlns":39},[41,19368,19369,19383],{},[44,19370,19371,19373,19375,19377,19379,19381],{},[47,19372,7634],{},[47,19374,6642],{},[51,19376,282],{},[47,19378,7634],{},[51,19380,10630],{},[47,19382,6642],{},[59,19384,19385],{"encoding":61},"IJ = I \\cap J",[28,19387,19389,19410,19428],{"className":19388,"ariaHidden":53},[66],[28,19390,19392,19395,19398,19401,19404,19407],{"className":19391},[70],[28,19393],{"className":19394,"style":154},[74],[28,19396,7634],{"className":19397,"style":7654},[79,80],[28,19399,6642],{"className":19400,"style":6663},[79,80],[28,19402],{"className":19403,"style":140},[89],[28,19405,282],{"className":19406},[144],[28,19408],{"className":19409,"style":140},[89],[28,19411,19413,19416,19419,19422,19425],{"className":19412},[70],[28,19414],{"className":19415,"style":154},[74],[28,19417,7634],{"className":19418,"style":7654},[79,80],[28,19420],{"className":19421,"style":363},[89],[28,19423,10630],{"className":19424},[367],[28,19426],{"className":19427,"style":363},[89],[28,19429,19431,19434],{"className":19430},[70],[28,19432],{"className":19433,"style":154},[74],[28,19435,6642],{"className":19436,"style":6663},[79,80],[28,19438,19440,19453],{"className":19439},[31],[28,19441,19443],{"className":19442},[35],[37,19444,19445],{"xmlns":39},[41,19446,19447,19451],{},[44,19448,19449],{},[47,19450,6532],{"mathvariant":191},[59,19452,6535],{"encoding":61},[28,19454,19456],{"className":19455,"ariaHidden":53},[66],[28,19457,19459,19462],{"className":19458},[70],[28,19460],{"className":19461,"style":6545},[74],[28,19463,6532],{"className":19464},[79,2120],[20,19466,19467,26,19470,15789,19498,18075,19673,19756,19757,9126,19785,19899,19900,20056,20057,20085],{},[23,19468,19469],{},"命题 3.3.5.",[28,19471,19473,19486],{"className":19472},[31],[28,19474,19476],{"className":19475},[35],[37,19477,19478],{"xmlns":39},[41,19479,19480,19484],{},[44,19481,19482],{},[47,19483,49],{},[59,19485,49],{"encoding":61},[28,19487,19489],{"className":19488,"ariaHidden":53},[66],[28,19490,19492,19495],{"className":19491},[70],[28,19493],{"className":19494,"style":154},[74],[28,19496,49],{"className":19497,"style":81},[79,80],[28,19499,19501,19539],{"className":19500},[31],[28,19502,19504],{"className":19503},[35],[37,19505,19506],{"xmlns":39},[41,19507,19508,19536],{},[44,19509,19510,19516,19518,19520,19522,19528,19530,19532,19534],{},[2621,19511,19512,19514],{},[47,19513,7634],{},[1731,19515,6706],{},[51,19517,54],{"separator":53},[51,19519,17172],{},[51,19521,54],{"separator":53},[2621,19523,19524,19526],{},[47,19525,7634],{},[47,19527,11123],{},[51,19529,54],{"separator":53},[47,19531,6642],{},[51,19533,2090],{},[47,19535,49],{},[59,19537,19538],{"encoding":61},"I_1, \\dots, I_k, J \\lhd R",[28,19540,19542,19664],{"className":19541,"ariaHidden":53},[66],[28,19543,19545,19548,19588,19591,19594,19597,19600,19603,19606,19646,19649,19652,19655,19658,19661],{"className":19544},[70],[28,19546],{"className":19547,"style":75},[74],[28,19549,19551,19554],{"className":19550},[79],[28,19552,7634],{"className":19553,"style":7654},[79,80],[28,19555,19557],{"className":19556},[2664],[28,19558,19560,19580],{"className":19559},[2668,2669],[28,19561,19563,19577],{"className":19562},[2673],[28,19564,19566],{"className":19565,"style":11486},[2677],[28,19567,19568,19571],{"style":15432},[28,19569],{"className":19570,"style":2686},[2685],[28,19572,19574],{"className":19573},[2690,2691,2692,2693],[28,19575,6706],{"className":19576},[79,2693],[28,19578,2701],{"className":19579},[2700],[28,19581,19583],{"className":19582},[2673],[28,19584,19586],{"className":19585,"style":2708},[2677],[28,19587],{},[28,19589,54],{"className":19590},[85],[28,19592],{"className":19593,"style":90},[89],[28,19595,17172],{"className":19596},[17246],[28,19598],{"className":19599,"style":90},[89],[28,19601,54],{"className":19602},[85],[28,19604],{"className":19605,"style":90},[89],[28,19607,19609,19612],{"className":19608},[79],[28,19610,7634],{"className":19611,"style":7654},[79,80],[28,19613,19615],{"className":19614},[2664],[28,19616,19618,19638],{"className":19617},[2668,2669],[28,19619,19621,19635],{"className":19620},[2673],[28,19622,19624],{"className":19623,"style":17274},[2677],[28,19625,19626,19629],{"style":15432},[28,19627],{"className":19628,"style":2686},[2685],[28,19630,19632],{"className":19631},[2690,2691,2692,2693],[28,19633,11123],{"className":19634,"style":11155},[79,80,2693],[28,19636,2701],{"className":19637},[2700],[28,19639,19641],{"className":19640},[2673],[28,19642,19644],{"className":19643,"style":2708},[2677],[28,19645],{},[28,19647,54],{"className":19648},[85],[28,19650],{"className":19651,"style":90},[89],[28,19653,6642],{"className":19654,"style":6663},[79,80],[28,19656],{"className":19657,"style":363},[89],[28,19659,2090],{"className":19660},[367,2120],[28,19662],{"className":19663,"style":363},[89],[28,19665,19667,19670],{"className":19666},[70],[28,19668],{"className":19669,"style":154},[74],[28,19671,49],{"className":19672,"style":81},[79,80],[28,19674,19676,19698],{"className":19675},[31],[28,19677,19679],{"className":19678},[35],[37,19680,19681],{"xmlns":39},[41,19682,19683,19695],{},[44,19684,19685,19691,19693],{},[2621,19686,19687,19689],{},[47,19688,7634],{},[47,19690,864],{},[51,19692,54],{"separator":53},[47,19694,6642],{},[59,19696,19697],{"encoding":61},"I_s, J",[28,19699,19701],{"className":19700,"ariaHidden":53},[66],[28,19702,19704,19707,19747,19750,19753],{"className":19703},[70],[28,19705],{"className":19706,"style":75},[74],[28,19708,19710,19713],{"className":19709},[79],[28,19711,7634],{"className":19712,"style":7654},[79,80],[28,19714,19716],{"className":19715},[2664],[28,19717,19719,19739],{"className":19718},[2668,2669],[28,19720,19722,19736],{"className":19721},[2673],[28,19723,19725],{"className":19724,"style":14481},[2677],[28,19726,19727,19730],{"style":15432},[28,19728],{"className":19729,"style":2686},[2685],[28,19731,19733],{"className":19732},[2690,2691,2692,2693],[28,19734,864],{"className":19735},[79,80,2693],[28,19737,2701],{"className":19738},[2700],[28,19740,19742],{"className":19741},[2673],[28,19743,19745],{"className":19744,"style":2708},[2677],[28,19746],{},[28,19748,54],{"className":19749},[85],[28,19751],{"className":19752,"style":90},[89],[28,19754,6642],{"className":19755,"style":6663},[79,80]," 都互素（即对于每个 ",[28,19758,19760,19773],{"className":19759},[31],[28,19761,19763],{"className":19762},[35],[37,19764,19765],{"xmlns":39},[41,19766,19767,19771],{},[44,19768,19769],{},[47,19770,864],{},[59,19772,864],{"encoding":61},[28,19774,19776],{"className":19775,"ariaHidden":53},[66],[28,19777,19779,19782],{"className":19778},[70],[28,19780],{"className":19781,"style":761},[74],[28,19783,864],{"className":19784},[79,80],[28,19786,19788,19814],{"className":19787},[31],[28,19789,19791],{"className":19790},[35],[37,19792,19793],{"xmlns":39},[41,19794,19795,19811],{},[44,19796,19797,19803,19805,19807,19809],{},[2621,19798,19799,19801],{},[47,19800,7634],{},[47,19802,864],{},[51,19804,274],{},[47,19806,6642],{},[51,19808,282],{},[47,19810,49],{},[59,19812,19813],{"encoding":61},"I_s+J=R",[28,19815,19817,19872,19890],{"className":19816,"ariaHidden":53},[66],[28,19818,19820,19823,19863,19866,19869],{"className":19819},[70],[28,19821],{"className":19822,"style":15411},[74],[28,19824,19826,19829],{"className":19825},[79],[28,19827,7634],{"className":19828,"style":7654},[79,80],[28,19830,19832],{"className":19831},[2664],[28,19833,19835,19855],{"className":19834},[2668,2669],[28,19836,19838,19852],{"className":19837},[2673],[28,19839,19841],{"className":19840,"style":14481},[2677],[28,19842,19843,19846],{"style":15432},[28,19844],{"className":19845,"style":2686},[2685],[28,19847,19849],{"className":19848},[2690,2691,2692,2693],[28,19850,864],{"className":19851},[79,80,2693],[28,19853,2701],{"className":19854},[2700],[28,19856,19858],{"className":19857},[2673],[28,19859,19861],{"className":19860,"style":2708},[2677],[28,19862],{},[28,19864],{"className":19865,"style":363},[89],[28,19867,274],{"className":19868},[367],[28,19870],{"className":19871,"style":363},[89],[28,19873,19875,19878,19881,19884,19887],{"className":19874},[70],[28,19876],{"className":19877,"style":154},[74],[28,19879,6642],{"className":19880,"style":6663},[79,80],[28,19882],{"className":19883,"style":140},[89],[28,19885,282],{"className":19886},[144],[28,19888],{"className":19889,"style":140},[89],[28,19891,19893,19896],{"className":19892},[70],[28,19894],{"className":19895,"style":154},[74],[28,19897,49],{"className":19898,"style":81},[79,80],"），则 ",[28,19901,19903,19933],{"className":19902},[31],[28,19904,19906],{"className":19905},[35],[37,19907,19908],{"xmlns":39},[41,19909,19910,19930],{},[44,19911,19912,19918,19920,19922,19924],{},[2621,19913,19914,19916],{},[47,19915,7634],{},[1731,19917,6706],{},[51,19919,10630],{},[51,19921,17336],{},[51,19923,10630],{},[2621,19925,19926,19928],{},[47,19927,7634],{},[47,19929,11123],{},[59,19931,19932],{"encoding":61},"I_1 \\cap \\dots \\cap I_k",[28,19934,19936,19991,20010],{"className":19935,"ariaHidden":53},[66],[28,19937,19939,19942,19982,19985,19988],{"className":19938},[70],[28,19940],{"className":19941,"style":15411},[74],[28,19943,19945,19948],{"className":19944},[79],[28,19946,7634],{"className":19947,"style":7654},[79,80],[28,19949,19951],{"className":19950},[2664],[28,19952,19954,19974],{"className":19953},[2668,2669],[28,19955,19957,19971],{"className":19956},[2673],[28,19958,19960],{"className":19959,"style":11486},[2677],[28,19961,19962,19965],{"style":15432},[28,19963],{"className":19964,"style":2686},[2685],[28,19966,19968],{"className":19967},[2690,2691,2692,2693],[28,19969,6706],{"className":19970},[79,2693],[28,19972,2701],{"className":19973},[2700],[28,19975,19977],{"className":19976},[2673],[28,19978,19980],{"className":19979,"style":2708},[2677],[28,19981],{},[28,19983],{"className":19984,"style":363},[89],[28,19986,10630],{"className":19987},[367],[28,19989],{"className":19990,"style":363},[89],[28,19992,19994,19998,20001,20004,20007],{"className":19993},[70],[28,19995],{"className":19996,"style":19997},[74],"height:0.5556em;",[28,19999,17336],{"className":20000},[17246],[28,20002],{"className":20003,"style":363},[89],[28,20005,10630],{"className":20006},[367],[28,20008],{"className":20009,"style":363},[89],[28,20011,20013,20016],{"className":20012},[70],[28,20014],{"className":20015,"style":15411},[74],[28,20017,20019,20022],{"className":20018},[79],[28,20020,7634],{"className":20021,"style":7654},[79,80],[28,20023,20025],{"className":20024},[2664],[28,20026,20028,20048],{"className":20027},[2668,2669],[28,20029,20031,20045],{"className":20030},[2673],[28,20032,20034],{"className":20033,"style":17274},[2677],[28,20035,20036,20039],{"style":15432},[28,20037],{"className":20038,"style":2686},[2685],[28,20040,20042],{"className":20041},[2690,2691,2692,2693],[28,20043,11123],{"className":20044,"style":11155},[79,80,2693],[28,20046,2701],{"className":20047},[2700],[28,20049,20051],{"className":20050},[2673],[28,20052,20054],{"className":20053,"style":2708},[2677],[28,20055],{}," 与 ",[28,20058,20060,20073],{"className":20059},[31],[28,20061,20063],{"className":20062},[35],[37,20064,20065],{"xmlns":39},[41,20066,20067,20071],{},[44,20068,20069],{},[47,20070,6642],{},[59,20072,6642],{"encoding":61},[28,20074,20076],{"className":20075,"ariaHidden":53},[66],[28,20077,20079,20082],{"className":20078},[70],[28,20080],{"className":20081,"style":154},[74],[28,20083,6642],{"className":20084,"style":6663},[79,80]," 也互素。",[20,20087,20088,20091,20092,20120],{},[23,20089,20090],{},"证明 (详细展开):","\n对 ",[28,20093,20095,20108],{"className":20094},[31],[28,20096,20098],{"className":20097},[35],[37,20099,20100],{"xmlns":39},[41,20101,20102,20106],{},[44,20103,20104],{},[47,20105,11123],{},[59,20107,11123],{"encoding":61},[28,20109,20111],{"className":20110,"ariaHidden":53},[66],[28,20112,20114,20117],{"className":20113},[70],[28,20115],{"className":20116,"style":780},[74],[28,20118,11123],{"className":20119,"style":11155},[79,80]," 用数学归纳法。",[1679,20122,20123,20177,20498],{},[545,20124,20125,20176],{},[28,20126,20128,20146],{"className":20127},[31],[28,20129,20131],{"className":20130},[35],[37,20132,20133],{"xmlns":39},[41,20134,20135,20143],{},[44,20136,20137,20139,20141],{},[47,20138,11123],{},[51,20140,282],{},[1731,20142,6706],{},[59,20144,20145],{"encoding":61},"k=1",[28,20147,20149,20167],{"className":20148,"ariaHidden":53},[66],[28,20150,20152,20155,20158,20161,20164],{"className":20151},[70],[28,20153],{"className":20154,"style":780},[74],[28,20156,11123],{"className":20157,"style":11155},[79,80],[28,20159],{"className":20160,"style":140},[89],[28,20162,282],{"className":20163},[144],[28,20165],{"className":20166,"style":140},[89],[28,20168,20170,20173],{"className":20169},[70],[28,20171],{"className":20172,"style":3176},[74],[28,20174,6706],{"className":20175},[79]," 时，由已知条件显然成立。",[545,20178,20179,20180,20231,20232,3062,20425,537],{},"假设 ",[28,20181,20183,20201],{"className":20182},[31],[28,20184,20186],{"className":20185},[35],[37,20187,20188],{"xmlns":39},[41,20189,20190,20198],{},[44,20191,20192,20194,20196],{},[47,20193,11123],{},[51,20195,3201],{},[1731,20197,6706],{},[59,20199,20200],{"encoding":61},"k-1",[28,20202,20204,20222],{"className":20203,"ariaHidden":53},[66],[28,20205,20207,20210,20213,20216,20219],{"className":20206},[70],[28,20208],{"className":20209,"style":8239},[74],[28,20211,11123],{"className":20212,"style":11155},[79,80],[28,20214],{"className":20215,"style":363},[89],[28,20217,3201],{"className":20218},[367],[28,20220],{"className":20221,"style":363},[89],[28,20223,20225,20228],{"className":20224},[70],[28,20226],{"className":20227,"style":3176},[74],[28,20229,6706],{"className":20230},[79]," 时结论成立，即设 ",[28,20233,20235,20275],{"className":20234},[31],[28,20236,20238],{"className":20237},[35],[37,20239,20240],{"xmlns":39},[41,20241,20242,20272],{},[44,20243,20244,20246,20248,20254,20256,20258,20260],{},[47,20245,14519],{},[51,20247,282],{},[2621,20249,20250,20252],{},[47,20251,7634],{},[1731,20253,6706],{},[51,20255,10630],{},[51,20257,17336],{},[51,20259,10630],{},[2621,20261,20262,20264],{},[47,20263,7634],{},[44,20265,20266,20268,20270],{},[47,20267,11123],{},[51,20269,3201],{},[1731,20271,6706],{},[59,20273,20274],{"encoding":61},"A = I_1 \\cap \\dots \\cap I_{k-1}",[28,20276,20278,20296,20351,20369],{"className":20277,"ariaHidden":53},[66],[28,20279,20281,20284,20287,20290,20293],{"className":20280},[70],[28,20282],{"className":20283,"style":154},[74],[28,20285,14519],{"className":20286},[79,80],[28,20288],{"className":20289,"style":140},[89],[28,20291,282],{"className":20292},[144],[28,20294],{"className":20295,"style":140},[89],[28,20297,20299,20302,20342,20345,20348],{"className":20298},[70],[28,20300],{"className":20301,"style":15411},[74],[28,20303,20305,20308],{"className":20304},[79],[28,20306,7634],{"className":20307,"style":7654},[79,80],[28,20309,20311],{"className":20310},[2664],[28,20312,20314,20334],{"className":20313},[2668,2669],[28,20315,20317,20331],{"className":20316},[2673],[28,20318,20320],{"className":20319,"style":11486},[2677],[28,20321,20322,20325],{"style":15432},[28,20323],{"className":20324,"style":2686},[2685],[28,20326,20328],{"className":20327},[2690,2691,2692,2693],[28,20329,6706],{"className":20330},[79,2693],[28,20332,2701],{"className":20333},[2700],[28,20335,20337],{"className":20336},[2673],[28,20338,20340],{"className":20339,"style":2708},[2677],[28,20341],{},[28,20343],{"className":20344,"style":363},[89],[28,20346,10630],{"className":20347},[367],[28,20349],{"className":20350,"style":363},[89],[28,20352,20354,20357,20360,20363,20366],{"className":20353},[70],[28,20355],{"className":20356,"style":19997},[74],[28,20358,17336],{"className":20359},[17246],[28,20361],{"className":20362,"style":363},[89],[28,20364,10630],{"className":20365},[367],[28,20367],{"className":20368,"style":363},[89],[28,20370,20372,20376],{"className":20371},[70],[28,20373],{"className":20374,"style":20375},[74],"height:0.8917em;vertical-align:-0.2083em;",[28,20377,20379,20382],{"className":20378},[79],[28,20380,7634],{"className":20381,"style":7654},[79,80],[28,20383,20385],{"className":20384},[2664],[28,20386,20388,20417],{"className":20387},[2668,2669],[28,20389,20391,20414],{"className":20390},[2673],[28,20392,20394],{"className":20393,"style":17274},[2677],[28,20395,20396,20399],{"style":15432},[28,20397],{"className":20398,"style":2686},[2685],[28,20400,20402],{"className":20401},[2690,2691,2692,2693],[28,20403,20405,20408,20411],{"className":20404},[79,2693],[28,20406,11123],{"className":20407,"style":11155},[79,80,2693],[28,20409,3201],{"className":20410},[367,2693],[28,20412,6706],{"className":20413},[79,2693],[28,20415,2701],{"className":20416},[2700],[28,20418,20420],{"className":20419},[2673],[28,20421,20423],{"className":20422,"style":17592},[2677],[28,20424],{},[28,20426,20428,20450],{"className":20427},[31],[28,20429,20431],{"className":20430},[35],[37,20432,20433],{"xmlns":39},[41,20434,20435,20447],{},[44,20436,20437,20439,20441,20443,20445],{},[47,20438,14519],{},[51,20440,274],{},[47,20442,6642],{},[51,20444,282],{},[47,20446,49],{},[59,20448,20449],{"encoding":61},"A+J=R",[28,20451,20453,20471,20489],{"className":20452,"ariaHidden":53},[66],[28,20454,20456,20459,20462,20465,20468],{"className":20455},[70],[28,20457],{"className":20458,"style":10649},[74],[28,20460,14519],{"className":20461},[79,80],[28,20463],{"className":20464,"style":363},[89],[28,20466,274],{"className":20467},[367],[28,20469],{"className":20470,"style":363},[89],[28,20472,20474,20477,20480,20483,20486],{"className":20473},[70],[28,20475],{"className":20476,"style":154},[74],[28,20478,6642],{"className":20479,"style":6663},[79,80],[28,20481],{"className":20482,"style":140},[89],[28,20484,282],{"className":20485},[144],[28,20487],{"className":20488,"style":140},[89],[28,20490,20492,20495],{"className":20491},[70],[28,20493],{"className":20494,"style":154},[74],[28,20496,49],{"className":20497,"style":81},[79,80],[545,20499,20500,20501,20529,20530,20624,20625,20697,20698,20771,20772,537,20877,20880,20881,20979,20980,21008,21009,21178,21179,21346,21347,21631,21633,21634,21997,21998,22103,22104,14206,22208,20056,22362,17115,22390],{},"现在考虑 ",[28,20502,20504,20517],{"className":20503},[31],[28,20505,20507],{"className":20506},[35],[37,20508,20509],{"xmlns":39},[41,20510,20511,20515],{},[44,20512,20513],{},[47,20514,11123],{},[59,20516,11123],{"encoding":61},[28,20518,20520],{"className":20519,"ariaHidden":53},[66],[28,20521,20523,20526],{"className":20522},[70],[28,20524],{"className":20525,"style":780},[74],[28,20527,11123],{"className":20528,"style":11155},[79,80]," 的情况。令 ",[28,20531,20533,20556],{"className":20532},[31],[28,20534,20536],{"className":20535},[35],[37,20537,20538],{"xmlns":39},[41,20539,20540,20553],{},[44,20541,20542,20545,20547],{},[47,20543,20544],{},"B",[51,20546,282],{},[2621,20548,20549,20551],{},[47,20550,7634],{},[47,20552,11123],{},[59,20554,20555],{"encoding":61},"B = I_k",[28,20557,20559,20578],{"className":20558,"ariaHidden":53},[66],[28,20560,20562,20565,20569,20572,20575],{"className":20561},[70],[28,20563],{"className":20564,"style":154},[74],[28,20566,20544],{"className":20567,"style":20568},[79,80],"margin-right:0.0502em;",[28,20570],{"className":20571,"style":140},[89],[28,20573,282],{"className":20574},[144],[28,20576],{"className":20577,"style":140},[89],[28,20579,20581,20584],{"className":20580},[70],[28,20582],{"className":20583,"style":15411},[74],[28,20585,20587,20590],{"className":20586},[79],[28,20588,7634],{"className":20589,"style":7654},[79,80],[28,20591,20593],{"className":20592},[2664],[28,20594,20596,20616],{"className":20595},[2668,2669],[28,20597,20599,20613],{"className":20598},[2673],[28,20600,20602],{"className":20601,"style":17274},[2677],[28,20603,20604,20607],{"style":15432},[28,20605],{"className":20606,"style":2686},[2685],[28,20608,20610],{"className":20609},[2690,2691,2692,2693],[28,20611,11123],{"className":20612,"style":11155},[79,80,2693],[28,20614,2701],{"className":20615},[2700],[28,20617,20619],{"className":20618},[2673],[28,20620,20622],{"className":20621,"style":2708},[2677],[28,20623],{},"。已知 ",[28,20626,20628,20649],{"className":20627},[31],[28,20629,20631],{"className":20630},[35],[37,20632,20633],{"xmlns":39},[41,20634,20635,20647],{},[44,20636,20637,20639,20641,20643,20645],{},[47,20638,14519],{},[51,20640,274],{},[47,20642,6642],{},[51,20644,282],{},[47,20646,49],{},[59,20648,20449],{"encoding":61},[28,20650,20652,20670,20688],{"className":20651,"ariaHidden":53},[66],[28,20653,20655,20658,20661,20664,20667],{"className":20654},[70],[28,20656],{"className":20657,"style":10649},[74],[28,20659,14519],{"className":20660},[79,80],[28,20662],{"className":20663,"style":363},[89],[28,20665,274],{"className":20666},[367],[28,20668],{"className":20669,"style":363},[89],[28,20671,20673,20676,20679,20682,20685],{"className":20672},[70],[28,20674],{"className":20675,"style":154},[74],[28,20677,6642],{"className":20678,"style":6663},[79,80],[28,20680],{"className":20681,"style":140},[89],[28,20683,282],{"className":20684},[144],[28,20686],{"className":20687,"style":140},[89],[28,20689,20691,20694],{"className":20690},[70],[28,20692],{"className":20693,"style":154},[74],[28,20695,49],{"className":20696,"style":81},[79,80]," 且 ",[28,20699,20701,20723],{"className":20700},[31],[28,20702,20704],{"className":20703},[35],[37,20705,20706],{"xmlns":39},[41,20707,20708,20720],{},[44,20709,20710,20712,20714,20716,20718],{},[47,20711,20544],{},[51,20713,274],{},[47,20715,6642],{},[51,20717,282],{},[47,20719,49],{},[59,20721,20722],{"encoding":61},"B+J=R",[28,20724,20726,20744,20762],{"className":20725,"ariaHidden":53},[66],[28,20727,20729,20732,20735,20738,20741],{"className":20728},[70],[28,20730],{"className":20731,"style":10649},[74],[28,20733,20544],{"className":20734,"style":20568},[79,80],[28,20736],{"className":20737,"style":363},[89],[28,20739,274],{"className":20740},[367],[28,20742],{"className":20743,"style":363},[89],[28,20745,20747,20750,20753,20756,20759],{"className":20746},[70],[28,20748],{"className":20749,"style":154},[74],[28,20751,6642],{"className":20752,"style":6663},[79,80],[28,20754],{"className":20755,"style":140},[89],[28,20757,282],{"className":20758},[144],[28,20760],{"className":20761,"style":140},[89],[28,20763,20765,20768],{"className":20764},[70],[28,20766],{"className":20767,"style":154},[74],[28,20769,49],{"className":20770,"style":81},[79,80],"。我们只需证明 ",[28,20773,20775,20805],{"className":20774},[31],[28,20776,20778],{"className":20777},[35],[37,20779,20780],{"xmlns":39},[41,20781,20782,20802],{},[44,20783,20784,20786,20788,20790,20792,20794,20796,20798,20800],{},[51,20785,269],{"stretchy":268},[47,20787,14519],{},[51,20789,10630],{},[47,20791,20544],{},[51,20793,279],{"stretchy":268},[51,20795,274],{},[47,20797,6642],{},[51,20799,282],{},[47,20801,49],{},[59,20803,20804],{"encoding":61},"(A \\cap B) + J = R",[28,20806,20808,20829,20850,20868],{"className":20807,"ariaHidden":53},[66],[28,20809,20811,20814,20817,20820,20823,20826],{"className":20810},[70],[28,20812],{"className":20813,"style":349},[74],[28,20815,269],{"className":20816},[356],[28,20818,14519],{"className":20819},[79,80],[28,20821],{"className":20822,"style":363},[89],[28,20824,10630],{"className":20825},[367],[28,20827],{"className":20828,"style":363},[89],[28,20830,20832,20835,20838,20841,20844,20847],{"className":20831},[70],[28,20833],{"className":20834,"style":349},[74],[28,20836,20544],{"className":20837,"style":20568},[79,80],[28,20839,279],{"className":20840},[383],[28,20842],{"className":20843,"style":363},[89],[28,20845,274],{"className":20846},[367],[28,20848],{"className":20849,"style":363},[89],[28,20851,20853,20856,20859,20862,20865],{"className":20852},[70],[28,20854],{"className":20855,"style":154},[74],[28,20857,6642],{"className":20858,"style":6663},[79,80],[28,20860],{"className":20861,"style":140},[89],[28,20863,282],{"className":20864},[144],[28,20866],{"className":20867,"style":140},[89],[28,20869,20871,20874],{"className":20870},[70],[28,20872],{"className":20873,"style":154},[74],[28,20875,49],{"className":20876,"style":81},[79,80],[20878,20879],"br",{},"考察乘积 ",[28,20882,20884,20916],{"className":20883},[31],[28,20885,20887],{"className":20886},[35],[37,20888,20889],{"xmlns":39},[41,20890,20891,20913],{},[44,20892,20893,20895,20897,20899,20901,20903,20905,20907,20909,20911],{},[51,20894,269],{"stretchy":268},[47,20896,14519],{},[51,20898,274],{},[47,20900,6642],{},[51,20902,279],{"stretchy":268},[51,20904,269],{"stretchy":268},[47,20906,20544],{},[51,20908,274],{},[47,20910,6642],{},[51,20912,279],{"stretchy":268},[59,20914,20915],{"encoding":61},"(A+J)(B+J)",[28,20917,20919,20940,20967],{"className":20918,"ariaHidden":53},[66],[28,20920,20922,20925,20928,20931,20934,20937],{"className":20921},[70],[28,20923],{"className":20924,"style":349},[74],[28,20926,269],{"className":20927},[356],[28,20929,14519],{"className":20930},[79,80],[28,20932],{"className":20933,"style":363},[89],[28,20935,274],{"className":20936},[367],[28,20938],{"className":20939,"style":363},[89],[28,20941,20943,20946,20949,20952,20955,20958,20961,20964],{"className":20942},[70],[28,20944],{"className":20945,"style":349},[74],[28,20947,6642],{"className":20948,"style":6663},[79,80],[28,20950,279],{"className":20951},[383],[28,20953,269],{"className":20954},[356],[28,20956,20544],{"className":20957,"style":20568},[79,80],[28,20959],{"className":20960,"style":363},[89],[28,20962,274],{"className":20963},[367],[28,20965],{"className":20966,"style":363},[89],[28,20968,20970,20973,20976],{"className":20969},[70],[28,20971],{"className":20972,"style":349},[74],[28,20974,6642],{"className":20975,"style":6663},[79,80],[28,20977,279],{"className":20978},[383],"。\n由于 ",[28,20981,20983,20996],{"className":20982},[31],[28,20984,20986],{"className":20985},[35],[37,20987,20988],{"xmlns":39},[41,20989,20990,20994],{},[44,20991,20992],{},[47,20993,49],{},[59,20995,49],{"encoding":61},[28,20997,20999],{"className":20998,"ariaHidden":53},[66],[28,21000,21002,21005],{"className":21001},[70],[28,21003],{"className":21004,"style":154},[74],[28,21006,49],{"className":21007,"style":81},[79,80]," 是幺环，\n",[28,21010,21012,21058],{"className":21011},[31],[28,21013,21015],{"className":21014},[35],[37,21016,21017],{"xmlns":39},[41,21018,21019,21055],{},[44,21020,21021,21023,21025,21027,21029,21031,21033,21035,21037,21039,21041,21043,21045,21047,21049,21051,21053],{},[47,21022,49],{},[51,21024,282],{},[47,21026,49],{},[51,21028,3732],{},[47,21030,49],{},[51,21032,282],{},[51,21034,269],{"stretchy":268},[47,21036,14519],{},[51,21038,274],{},[47,21040,6642],{},[51,21042,279],{"stretchy":268},[51,21044,269],{"stretchy":268},[47,21046,20544],{},[51,21048,274],{},[47,21050,6642],{},[51,21052,279],{"stretchy":268},[47,21054,336],{"mathvariant":191},[59,21056,21057],{"encoding":61},"R = R \\cdot R = (A+J)(B+J).",[28,21059,21061,21079,21097,21115,21136,21163],{"className":21060,"ariaHidden":53},[66],[28,21062,21064,21067,21070,21073,21076],{"className":21063},[70],[28,21065],{"className":21066,"style":154},[74],[28,21068,49],{"className":21069,"style":81},[79,80],[28,21071],{"className":21072,"style":140},[89],[28,21074,282],{"className":21075},[144],[28,21077],{"className":21078,"style":140},[89],[28,21080,21082,21085,21088,21091,21094],{"className":21081},[70],[28,21083],{"className":21084,"style":154},[74],[28,21086,49],{"className":21087,"style":81},[79,80],[28,21089],{"className":21090,"style":363},[89],[28,21092,3732],{"className":21093},[367],[28,21095],{"className":21096,"style":363},[89],[28,21098,21100,21103,21106,21109,21112],{"className":21099},[70],[28,21101],{"className":21102,"style":154},[74],[28,21104,49],{"className":21105,"style":81},[79,80],[28,21107],{"className":21108,"style":140},[89],[28,21110,282],{"className":21111},[144],[28,21113],{"className":21114,"style":140},[89],[28,21116,21118,21121,21124,21127,21130,21133],{"className":21117},[70],[28,21119],{"className":21120,"style":349},[74],[28,21122,269],{"className":21123},[356],[28,21125,14519],{"className":21126},[79,80],[28,21128],{"className":21129,"style":363},[89],[28,21131,274],{"className":21132},[367],[28,21134],{"className":21135,"style":363},[89],[28,21137,21139,21142,21145,21148,21151,21154,21157,21160],{"className":21138},[70],[28,21140],{"className":21141,"style":349},[74],[28,21143,6642],{"className":21144,"style":6663},[79,80],[28,21146,279],{"className":21147},[383],[28,21149,269],{"className":21150},[356],[28,21152,20544],{"className":21153,"style":20568},[79,80],[28,21155],{"className":21156,"style":363},[89],[28,21158,274],{"className":21159},[367],[28,21161],{"className":21162,"style":363},[89],[28,21164,21166,21169,21172,21175],{"className":21165},[70],[28,21167],{"className":21168,"style":349},[74],[28,21170,6642],{"className":21171,"style":6663},[79,80],[28,21173,279],{"className":21174},[383],[28,21176,336],{"className":21177},[79],"\n展开上式（利用理想加法和乘法的分配律）：\n",[28,21180,21182,21224],{"className":21181},[31],[28,21183,21185],{"className":21184},[35],[37,21186,21187],{"xmlns":39},[41,21188,21189,21221],{},[44,21190,21191,21193,21195,21197,21199,21201,21203,21205,21207,21209,21211,21213,21219],{},[47,21192,49],{},[51,21194,282],{},[47,21196,14519],{},[47,21198,20544],{},[51,21200,274],{},[47,21202,14519],{},[47,21204,6642],{},[51,21206,274],{},[47,21208,6642],{},[47,21210,20544],{},[51,21212,274],{},[6696,21214,21215,21217],{},[47,21216,6642],{},[1731,21218,11448],{},[47,21220,336],{"mathvariant":191},[59,21222,21223],{"encoding":61},"R = AB + AJ + JB + J^2.",[28,21225,21227,21245,21266,21287,21308],{"className":21226,"ariaHidden":53},[66],[28,21228,21230,21233,21236,21239,21242],{"className":21229},[70],[28,21231],{"className":21232,"style":154},[74],[28,21234,49],{"className":21235,"style":81},[79,80],[28,21237],{"className":21238,"style":140},[89],[28,21240,282],{"className":21241},[144],[28,21243],{"className":21244,"style":140},[89],[28,21246,21248,21251,21254,21257,21260,21263],{"className":21247},[70],[28,21249],{"className":21250,"style":10649},[74],[28,21252,14519],{"className":21253},[79,80],[28,21255,20544],{"className":21256,"style":20568},[79,80],[28,21258],{"className":21259,"style":363},[89],[28,21261,274],{"className":21262},[367],[28,21264],{"className":21265,"style":363},[89],[28,21267,21269,21272,21275,21278,21281,21284],{"className":21268},[70],[28,21270],{"className":21271,"style":10649},[74],[28,21273,14519],{"className":21274},[79,80],[28,21276,6642],{"className":21277,"style":6663},[79,80],[28,21279],{"className":21280,"style":363},[89],[28,21282,274],{"className":21283},[367],[28,21285],{"className":21286,"style":363},[89],[28,21288,21290,21293,21296,21299,21302,21305],{"className":21289},[70],[28,21291],{"className":21292,"style":10649},[74],[28,21294,6642],{"className":21295,"style":6663},[79,80],[28,21297,20544],{"className":21298,"style":20568},[79,80],[28,21300],{"className":21301,"style":363},[89],[28,21303,274],{"className":21304},[367],[28,21306],{"className":21307,"style":363},[89],[28,21309,21311,21314,21343],{"className":21310},[70],[28,21312],{"className":21313,"style":6774},[74],[28,21315,21317,21320],{"className":21316},[79],[28,21318,6642],{"className":21319,"style":6663},[79,80],[28,21321,21323],{"className":21322},[2664],[28,21324,21326],{"className":21325},[2668],[28,21327,21329],{"className":21328},[2673],[28,21330,21332],{"className":21331,"style":6774},[2677],[28,21333,21334,21337],{"style":6777},[28,21335],{"className":21336,"style":2686},[2685],[28,21338,21340],{"className":21339},[2690,2691,2692,2693],[28,21341,11448],{"className":21342},[79,2693],[28,21344,336],{"className":21345},[79],"\n分析各项的包含关系：",[542,21348,21349,21430,21489,21547],{},[545,21350,21351,21429],{},[28,21352,21354,21378],{"className":21353},[31],[28,21355,21357],{"className":21356},[35],[37,21358,21359],{"xmlns":39},[41,21360,21361,21375],{},[44,21362,21363,21365,21367,21369,21371,21373],{},[47,21364,14519],{},[47,21366,20544],{},[51,21368,11216],{},[47,21370,14519],{},[51,21372,10630],{},[47,21374,20544],{},[59,21376,21377],{"encoding":61},"AB \\subseteq A \\cap B",[28,21379,21381,21402,21420],{"className":21380,"ariaHidden":53},[66],[28,21382,21384,21387,21390,21393,21396,21399],{"className":21383},[70],[28,21385],{"className":21386,"style":9234},[74],[28,21388,14519],{"className":21389},[79,80],[28,21391,20544],{"className":21392,"style":20568},[79,80],[28,21394],{"className":21395,"style":140},[89],[28,21397,11216],{"className":21398},[144],[28,21400],{"className":21401,"style":140},[89],[28,21403,21405,21408,21411,21414,21417],{"className":21404},[70],[28,21406],{"className":21407,"style":154},[74],[28,21409,14519],{"className":21410},[79,80],[28,21412],{"className":21413,"style":363},[89],[28,21415,10630],{"className":21416},[367],[28,21418],{"className":21419,"style":363},[89],[28,21421,21423,21426],{"className":21422},[70],[28,21424],{"className":21425,"style":154},[74],[28,21427,20544],{"className":21428,"style":20568},[79,80]," (两个理想的积总是包含在交集中)。",[545,21431,21432,21488],{},[28,21433,21435,21455],{"className":21434},[31],[28,21436,21438],{"className":21437},[35],[37,21439,21440],{"xmlns":39},[41,21441,21442,21452],{},[44,21443,21444,21446,21448,21450],{},[47,21445,14519],{},[47,21447,6642],{},[51,21449,11216],{},[47,21451,6642],{},[59,21453,21454],{"encoding":61},"AJ \\subseteq J",[28,21456,21458,21479],{"className":21457,"ariaHidden":53},[66],[28,21459,21461,21464,21467,21470,21473,21476],{"className":21460},[70],[28,21462],{"className":21463,"style":9234},[74],[28,21465,14519],{"className":21466},[79,80],[28,21468,6642],{"className":21469,"style":6663},[79,80],[28,21471],{"className":21472,"style":140},[89],[28,21474,11216],{"className":21475},[144],[28,21477],{"className":21478,"style":140},[89],[28,21480,21482,21485],{"className":21481},[70],[28,21483],{"className":21484,"style":154},[74],[28,21486,6642],{"className":21487,"style":6663},[79,80]," (理想的定义)。",[545,21490,21491,537],{},[28,21492,21494,21514],{"className":21493},[31],[28,21495,21497],{"className":21496},[35],[37,21498,21499],{"xmlns":39},[41,21500,21501,21511],{},[44,21502,21503,21505,21507,21509],{},[47,21504,6642],{},[47,21506,20544],{},[51,21508,11216],{},[47,21510,6642],{},[59,21512,21513],{"encoding":61},"JB \\subseteq J",[28,21515,21517,21538],{"className":21516,"ariaHidden":53},[66],[28,21518,21520,21523,21526,21529,21532,21535],{"className":21519},[70],[28,21521],{"className":21522,"style":9234},[74],[28,21524,6642],{"className":21525,"style":6663},[79,80],[28,21527,20544],{"className":21528,"style":20568},[79,80],[28,21530],{"className":21531,"style":140},[89],[28,21533,11216],{"className":21534},[144],[28,21536],{"className":21537,"style":140},[89],[28,21539,21541,21544],{"className":21540},[70],[28,21542],{"className":21543,"style":154},[74],[28,21545,6642],{"className":21546,"style":6663},[79,80],[545,21548,21549,537],{},[28,21550,21552,21574],{"className":21551},[31],[28,21553,21555],{"className":21554},[35],[37,21556,21557],{"xmlns":39},[41,21558,21559,21571],{},[44,21560,21561,21567,21569],{},[6696,21562,21563,21565],{},[47,21564,6642],{},[1731,21566,11448],{},[51,21568,11216],{},[47,21570,6642],{},[59,21572,21573],{"encoding":61},"J^2 \\subseteq J",[28,21575,21577,21622],{"className":21576,"ariaHidden":53},[66],[28,21578,21580,21584,21613,21616,21619],{"className":21579},[70],[28,21581],{"className":21582,"style":21583},[74],"height:0.9501em;vertical-align:-0.136em;",[28,21585,21587,21590],{"className":21586},[79],[28,21588,6642],{"className":21589,"style":6663},[79,80],[28,21591,21593],{"className":21592},[2664],[28,21594,21596],{"className":21595},[2668],[28,21597,21599],{"className":21598},[2673],[28,21600,21602],{"className":21601,"style":6774},[2677],[28,21603,21604,21607],{"style":6777},[28,21605],{"className":21606,"style":2686},[2685],[28,21608,21610],{"className":21609},[2690,2691,2692,2693],[28,21611,11448],{"className":21612},[79,2693],[28,21614],{"className":21615,"style":140},[89],[28,21617,11216],{"className":21618},[144],[28,21620],{"className":21621,"style":140},[89],[28,21623,21625,21628],{"className":21624},[70],[28,21626],{"className":21627,"style":154},[74],[28,21629,6642],{"className":21630,"style":6663},[79,80],[20878,21632],{},"因此，\n",[28,21635,21637,21719],{"className":21636},[31],[28,21638,21640],{"className":21639},[35],[37,21641,21642],{"xmlns":39},[41,21643,21644,21716],{},[44,21645,21646,21648,21650,21652,21654,21656,21658,21660,21662,21664,21666,21668,21674,21676,21678,21680,21682,21684,21686,21688,21690,21692,21694,21696,21698,21700,21702,21704,21706,21708,21710,21712,21714],{},[47,21647,49],{},[51,21649,282],{},[47,21651,14519],{},[47,21653,20544],{},[51,21655,274],{},[47,21657,14519],{},[47,21659,6642],{},[51,21661,274],{},[47,21663,6642],{},[47,21665,20544],{},[51,21667,274],{},[6696,21669,21670,21672],{},[47,21671,6642],{},[1731,21673,11448],{},[51,21675,11216],{},[51,21677,269],{"stretchy":268},[47,21679,14519],{},[51,21681,10630],{},[47,21683,20544],{},[51,21685,279],{"stretchy":268},[51,21687,274],{},[47,21689,6642],{},[51,21691,274],{},[47,21693,6642],{},[51,21695,274],{},[47,21697,6642],{},[51,21699,282],{},[51,21701,269],{"stretchy":268},[47,21703,14519],{},[51,21705,10630],{},[47,21707,20544],{},[51,21709,279],{"stretchy":268},[51,21711,274],{},[47,21713,6642],{},[47,21715,336],{"mathvariant":191},[59,21717,21718],{"encoding":61},"R = AB + AJ + JB + J^2 \\subseteq (A \\cap B) + J + J + J = (A \\cap B) + J.",[28,21720,21722,21740,21761,21782,21803,21847,21868,21889,21907,21925,21943,21964,21985],{"className":21721,"ariaHidden":53},[66],[28,21723,21725,21728,21731,21734,21737],{"className":21724},[70],[28,21726],{"className":21727,"style":154},[74],[28,21729,49],{"className":21730,"style":81},[79,80],[28,21732],{"className":21733,"style":140},[89],[28,21735,282],{"className":21736},[144],[28,21738],{"className":21739,"style":140},[89],[28,21741,21743,21746,21749,21752,21755,21758],{"className":21742},[70],[28,21744],{"className":21745,"style":10649},[74],[28,21747,14519],{"className":21748},[79,80],[28,21750,20544],{"className":21751,"style":20568},[79,80],[28,21753],{"className":21754,"style":363},[89],[28,21756,274],{"className":21757},[367],[28,21759],{"className":21760,"style":363},[89],[28,21762,21764,21767,21770,21773,21776,21779],{"className":21763},[70],[28,21765],{"className":21766,"style":10649},[74],[28,21768,14519],{"className":21769},[79,80],[28,21771,6642],{"className":21772,"style":6663},[79,80],[28,21774],{"className":21775,"style":363},[89],[28,21777,274],{"className":21778},[367],[28,21780],{"className":21781,"style":363},[89],[28,21783,21785,21788,21791,21794,21797,21800],{"className":21784},[70],[28,21786],{"className":21787,"style":10649},[74],[28,21789,6642],{"className":21790,"style":6663},[79,80],[28,21792,20544],{"className":21793,"style":20568},[79,80],[28,21795],{"className":21796,"style":363},[89],[28,21798,274],{"className":21799},[367],[28,21801],{"className":21802,"style":363},[89],[28,21804,21806,21809,21838,21841,21844],{"className":21805},[70],[28,21807],{"className":21808,"style":21583},[74],[28,21810,21812,21815],{"className":21811},[79],[28,21813,6642],{"className":21814,"style":6663},[79,80],[28,21816,21818],{"className":21817},[2664],[28,21819,21821],{"className":21820},[2668],[28,21822,21824],{"className":21823},[2673],[28,21825,21827],{"className":21826,"style":6774},[2677],[28,21828,21829,21832],{"style":6777},[28,21830],{"className":21831,"style":2686},[2685],[28,21833,21835],{"className":21834},[2690,2691,2692,2693],[28,21836,11448],{"className":21837},[79,2693],[28,21839],{"className":21840,"style":140},[89],[28,21842,11216],{"className":21843},[144],[28,21845],{"className":21846,"style":140},[89],[28,21848,21850,21853,21856,21859,21862,21865],{"className":21849},[70],[28,21851],{"className":21852,"style":349},[74],[28,21854,269],{"className":21855},[356],[28,21857,14519],{"className":21858},[79,80],[28,21860],{"className":21861,"style":363},[89],[28,21863,10630],{"className":21864},[367],[28,21866],{"className":21867,"style":363},[89],[28,21869,21871,21874,21877,21880,21883,21886],{"className":21870},[70],[28,21872],{"className":21873,"style":349},[74],[28,21875,20544],{"className":21876,"style":20568},[79,80],[28,21878,279],{"className":21879},[383],[28,21881],{"className":21882,"style":363},[89],[28,21884,274],{"className":21885},[367],[28,21887],{"className":21888,"style":363},[89],[28,21890,21892,21895,21898,21901,21904],{"className":21891},[70],[28,21893],{"className":21894,"style":10649},[74],[28,21896,6642],{"className":21897,"style":6663},[79,80],[28,21899],{"className":21900,"style":363},[89],[28,21902,274],{"className":21903},[367],[28,21905],{"className":21906,"style":363},[89],[28,21908,21910,21913,21916,21919,21922],{"className":21909},[70],[28,21911],{"className":21912,"style":10649},[74],[28,21914,6642],{"className":21915,"style":6663},[79,80],[28,21917],{"className":21918,"style":363},[89],[28,21920,274],{"className":21921},[367],[28,21923],{"className":21924,"style":363},[89],[28,21926,21928,21931,21934,21937,21940],{"className":21927},[70],[28,21929],{"className":21930,"style":154},[74],[28,21932,6642],{"className":21933,"style":6663},[79,80],[28,21935],{"className":21936,"style":140},[89],[28,21938,282],{"className":21939},[144],[28,21941],{"className":21942,"style":140},[89],[28,21944,21946,21949,21952,21955,21958,21961],{"className":21945},[70],[28,21947],{"className":21948,"style":349},[74],[28,21950,269],{"className":21951},[356],[28,21953,14519],{"className":21954},[79,80],[28,21956],{"className":21957,"style":363},[89],[28,21959,10630],{"className":21960},[367],[28,21962],{"className":21963,"style":363},[89],[28,21965,21967,21970,21973,21976,21979,21982],{"className":21966},[70],[28,21968],{"className":21969,"style":349},[74],[28,21971,20544],{"className":21972,"style":20568},[79,80],[28,21974,279],{"className":21975},[383],[28,21977],{"className":21978,"style":363},[89],[28,21980,274],{"className":21981},[367],[28,21983],{"className":21984,"style":363},[89],[28,21986,21988,21991,21994],{"className":21987},[70],[28,21989],{"className":21990,"style":154},[74],[28,21992,6642],{"className":21993,"style":6663},[79,80],[28,21995,336],{"className":21996},[79],"\n显然 ",[28,21999,22001,22031],{"className":22000},[31],[28,22002,22004],{"className":22003},[35],[37,22005,22006],{"xmlns":39},[41,22007,22008,22028],{},[44,22009,22010,22012,22014,22016,22018,22020,22022,22024,22026],{},[51,22011,269],{"stretchy":268},[47,22013,14519],{},[51,22015,10630],{},[47,22017,20544],{},[51,22019,279],{"stretchy":268},[51,22021,274],{},[47,22023,6642],{},[51,22025,11216],{},[47,22027,49],{},[59,22029,22030],{"encoding":61},"(A \\cap B) + J \\subseteq R",[28,22032,22034,22055,22076,22094],{"className":22033,"ariaHidden":53},[66],[28,22035,22037,22040,22043,22046,22049,22052],{"className":22036},[70],[28,22038],{"className":22039,"style":349},[74],[28,22041,269],{"className":22042},[356],[28,22044,14519],{"className":22045},[79,80],[28,22047],{"className":22048,"style":363},[89],[28,22050,10630],{"className":22051},[367],[28,22053],{"className":22054,"style":363},[89],[28,22056,22058,22061,22064,22067,22070,22073],{"className":22057},[70],[28,22059],{"className":22060,"style":349},[74],[28,22062,20544],{"className":22063,"style":20568},[79,80],[28,22065,279],{"className":22066},[383],[28,22068],{"className":22069,"style":363},[89],[28,22071,274],{"className":22072},[367],[28,22074],{"className":22075,"style":363},[89],[28,22077,22079,22082,22085,22088,22091],{"className":22078},[70],[28,22080],{"className":22081,"style":9234},[74],[28,22083,6642],{"className":22084,"style":6663},[79,80],[28,22086],{"className":22087,"style":140},[89],[28,22089,11216],{"className":22090},[144],[28,22092],{"className":22093,"style":140},[89],[28,22095,22097,22100],{"className":22096},[70],[28,22098],{"className":22099,"style":154},[74],[28,22101,49],{"className":22102,"style":81},[79,80],"。\n故 ",[28,22105,22107,22136],{"className":22106},[31],[28,22108,22110],{"className":22109},[35],[37,22111,22112],{"xmlns":39},[41,22113,22114,22134],{},[44,22115,22116,22118,22120,22122,22124,22126,22128,22130,22132],{},[51,22117,269],{"stretchy":268},[47,22119,14519],{},[51,22121,10630],{},[47,22123,20544],{},[51,22125,279],{"stretchy":268},[51,22127,274],{},[47,22129,6642],{},[51,22131,282],{},[47,22133,49],{},[59,22135,20804],{"encoding":61},[28,22137,22139,22160,22181,22199],{"className":22138,"ariaHidden":53},[66],[28,22140,22142,22145,22148,22151,22154,22157],{"className":22141},[70],[28,22143],{"className":22144,"style":349},[74],[28,22146,269],{"className":22147},[356],[28,22149,14519],{"className":22150},[79,80],[28,22152],{"className":22153,"style":363},[89],[28,22155,10630],{"className":22156},[367],[28,22158],{"className":22159,"style":363},[89],[28,22161,22163,22166,22169,22172,22175,22178],{"className":22162},[70],[28,22164],{"className":22165,"style":349},[74],[28,22167,20544],{"className":22168,"style":20568},[79,80],[28,22170,279],{"className":22171},[383],[28,22173],{"className":22174,"style":363},[89],[28,22176,274],{"className":22177},[367],[28,22179],{"className":22180,"style":363},[89],[28,22182,22184,22187,22190,22193,22196],{"className":22183},[70],[28,22185],{"className":22186,"style":154},[74],[28,22188,6642],{"className":22189,"style":6663},[79,80],[28,22191],{"className":22192,"style":140},[89],[28,22194,282],{"className":22195},[144],[28,22197],{"className":22198,"style":140},[89],[28,22200,22202,22205],{"className":22201},[70],[28,22203],{"className":22204,"style":154},[74],[28,22206,49],{"className":22207,"style":81},[79,80],[28,22209,22211,22240],{"className":22210},[31],[28,22212,22214],{"className":22213},[35],[37,22215,22216],{"xmlns":39},[41,22217,22218,22238],{},[44,22219,22220,22226,22228,22230,22232],{},[2621,22221,22222,22224],{},[47,22223,7634],{},[1731,22225,6706],{},[51,22227,10630],{},[51,22229,17336],{},[51,22231,10630],{},[2621,22233,22234,22236],{},[47,22235,7634],{},[47,22237,11123],{},[59,22239,19932],{"encoding":61},[28,22241,22243,22298,22316],{"className":22242,"ariaHidden":53},[66],[28,22244,22246,22249,22289,22292,22295],{"className":22245},[70],[28,22247],{"className":22248,"style":15411},[74],[28,22250,22252,22255],{"className":22251},[79],[28,22253,7634],{"className":22254,"style":7654},[79,80],[28,22256,22258],{"className":22257},[2664],[28,22259,22261,22281],{"className":22260},[2668,2669],[28,22262,22264,22278],{"className":22263},[2673],[28,22265,22267],{"className":22266,"style":11486},[2677],[28,22268,22269,22272],{"style":15432},[28,22270],{"className":22271,"style":2686},[2685],[28,22273,22275],{"className":22274},[2690,2691,2692,2693],[28,22276,6706],{"className":22277},[79,2693],[28,22279,2701],{"className":22280},[2700],[28,22282,22284],{"className":22283},[2673],[28,22285,22287],{"className":22286,"style":2708},[2677],[28,22288],{},[28,22290],{"className":22291,"style":363},[89],[28,22293,10630],{"className":22294},[367],[28,22296],{"className":22297,"style":363},[89],[28,22299,22301,22304,22307,22310,22313],{"className":22300},[70],[28,22302],{"className":22303,"style":19997},[74],[28,22305,17336],{"className":22306},[17246],[28,22308],{"className":22309,"style":363},[89],[28,22311,10630],{"className":22312},[367],[28,22314],{"className":22315,"style":363},[89],[28,22317,22319,22322],{"className":22318},[70],[28,22320],{"className":22321,"style":15411},[74],[28,22323,22325,22328],{"className":22324},[79],[28,22326,7634],{"className":22327,"style":7654},[79,80],[28,22329,22331],{"className":22330},[2664],[28,22332,22334,22354],{"className":22333},[2668,2669],[28,22335,22337,22351],{"className":22336},[2673],[28,22338,22340],{"className":22339,"style":17274},[2677],[28,22341,22342,22345],{"style":15432},[28,22343],{"className":22344,"style":2686},[2685],[28,22346,22348],{"className":22347},[2690,2691,2692,2693],[28,22349,11123],{"className":22350,"style":11155},[79,80,2693],[28,22352,2701],{"className":22353},[2700],[28,22355,22357],{"className":22356},[2673],[28,22358,22360],{"className":22359,"style":2708},[2677],[28,22361],{},[28,22363,22365,22378],{"className":22364},[31],[28,22366,22368],{"className":22367},[35],[37,22369,22370],{"xmlns":39},[41,22371,22372,22376],{},[44,22373,22374],{},[47,22375,6642],{},[59,22377,6642],{"encoding":61},[28,22379,22381],{"className":22380,"ariaHidden":53},[66],[28,22382,22384,22387],{"className":22383},[70],[28,22385],{"className":22386,"style":154},[74],[28,22388,6642],{"className":22389,"style":6663},[79,80],[28,22391,22393,22406],{"className":22392},[31],[28,22394,22396],{"className":22395},[35],[37,22397,22398],{"xmlns":39},[41,22399,22400,22404],{},[44,22401,22402],{},[47,22403,6532],{"mathvariant":191},[59,22405,6535],{"encoding":61},[28,22407,22409],{"className":22408,"ariaHidden":53},[66],[28,22410,22412,22415],{"className":22411},[70],[28,22413],{"className":22414,"style":6545},[74],[28,22416,6532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3.3.2.",[28,22424,22426,22439],{"className":22425},[31],[28,22427,22429],{"className":22428},[35],[37,22430,22431],{"xmlns":39},[41,22432,22433,22437],{},[44,22434,22435],{},[47,22436,49],{},[59,22438,49],{"encoding":61},[28,22440,22442],{"className":22441,"ariaHidden":53},[66],[28,22443,22445,22448],{"className":22444},[70],[28,22446],{"className":22447,"style":154},[74],[28,22449,49],{"className":22450,"style":81},[79,80],[28,22452,22454,22491],{"className":22453},[31],[28,22455,22457],{"className":22456},[35],[37,22458,22459],{"xmlns":39},[41,22460,22461,22489],{},[44,22462,22463,22469,22471,22473,22475,22481,22483,22485,22487],{},[2621,22464,22465,22467],{},[47,22466,7634],{},[1731,22468,6706],{},[51,22470,54],{"separator":53},[51,22472,17172],{},[51,22474,54],{"separator":53},[2621,22476,22477,22479],{},[47,22478,7634],{},[47,22480,11123],{},[51,22482,54],{"separator":53},[47,22484,6642],{},[51,22486,2090],{},[47,22488,49],{},[59,22490,19538],{"encoding":61},[28,22492,22494,22616],{"className":22493,"ariaHidden":53},[66],[28,22495,22497,22500,22540,22543,22546,22549,22552,22555,22558,22598,22601,22604,22607,22610,22613],{"className":22496},[70],[28,22498],{"className":22499,"style":75},[74],[28,22501,22503,22506],{"className":22502},[79],[28,22504,7634],{"className":22505,"style":7654},[79,80],[28,22507,22509],{"className":22508},[2664],[28,22510,22512,22532],{"className":22511},[2668,2669],[28,22513,22515,22529],{"className":22514},[2673],[28,22516,22518],{"className":22517,"style":11486},[2677],[28,22519,22520,22523],{"style":15432},[28,22521],{"className":22522,"style":2686},[2685],[28,22524,22526],{"className":22525},[2690,2691,2692,2693],[28,22527,6706],{"className":22528},[79,2693],[28,22530,2701],{"className":22531},[2700],[28,22533,22535],{"className":22534},[2673],[28,22536,22538],{"className":22537,"style":2708},[2677],[28,22539],{},[28,22541,54],{"className":22542},[85],[28,22544],{"className":22545,"style":90},[89],[28,22547,17172],{"className":22548},[17246],[28,22550],{"className":22551,"style":90},[89],[28,22553,54],{"className":22554},[85],[28,22556],{"className":22557,"style":90},[89],[28,22559,22561,22564],{"className":22560},[79],[28,22562,7634],{"className":22563,"style":7654},[79,80],[28,22565,22567],{"className":22566},[2664],[28,22568,22570,22590],{"className":22569},[2668,2669],[28,22571,22573,22587],{"className":22572},[2673],[28,22574,22576],{"className":22575,"style":17274},[2677],[28,22577,22578,22581],{"style":15432},[28,22579],{"className":22580,"style":2686},[2685],[28,22582,22584],{"className":22583},[2690,2691,2692,2693],[28,22585,11123],{"className":22586,"style":11155},[79,80,2693],[28,22588,2701],{"className":22589},[2700],[28,22591,22593],{"className":22592},[2673],[28,22594,22596],{"className":22595,"style":2708},[2677],[28,22597],{},[28,22599,54],{"className":22600},[85],[28,22602],{"className":22603,"style":90},[89],[28,22605,6642],{"className":22606,"style":6663},[79,80],[28,22608],{"className":22609,"style":363},[89],[28,22611,2090],{"className":22612},[367,2120],[28,22614],{"className":22615,"style":363},[89],[28,22617,22619,22622],{"className":22618},[70],[28,22620],{"className":22621,"style":154},[74],[28,22623,49],{"className":22624,"style":81},[79,80],[28,22626,22628,22649],{"className":22627},[31],[28,22629,22631],{"className":22630},[35],[37,22632,22633],{"xmlns":39},[41,22634,22635,22647],{},[44,22636,22637,22643,22645],{},[2621,22638,22639,22641],{},[47,22640,7634],{},[47,22642,864],{},[51,22644,54],{"separator":53},[47,22646,6642],{},[59,22648,19697],{"encoding":61},[28,22650,22652],{"className":22651,"ariaHidden":53},[66],[28,22653,22655,22658,22698,22701,22704],{"className":22654},[70],[28,22656],{"className":22657,"style":75},[74],[28,22659,22661,22664],{"className":22660},[79],[28,22662,7634],{"className":22663,"style":7654},[79,80],[28,22665,22667],{"className":22666},[2664],[28,22668,22670,22690],{"className":22669},[2668,2669],[28,22671,22673,22687],{"className":22672},[2673],[28,22674,22676],{"className":22675,"style":14481},[2677],[28,22677,22678,22681],{"style":15432},[28,22679],{"className":22680,"style":2686},[2685],[28,22682,22684],{"className":22683},[2690,2691,2692,2693],[28,22685,864],{"className":22686},[79,80,2693],[28,22688,2701],{"className":22689},[2700],[28,22691,22693],{"className":22692},[2673],[28,22694,22696],{"className":22695,"style":2708},[2677],[28,22697],{},[28,22699,54],{"className":22700},[85],[28,22702],{"className":22703,"style":90},[89],[28,22705,6642],{"className":22706,"style":6663},[79,80]," 都互素，则 ",[28,22709,22711,22737],{"className":22710},[31],[28,22712,22714],{"className":22713},[35],[37,22715,22716],{"xmlns":39},[41,22717,22718,22734],{},[44,22719,22720,22726,22728],{},[2621,22721,22722,22724],{},[47,22723,7634],{},[1731,22725,6706],{},[51,22727,17336],{},[2621,22729,22730,22732],{},[47,22731,7634],{},[47,22733,11123],{},[59,22735,22736],{"encoding":61},"I_1 \\cdots I_k",[28,22738,22740],{"className":22739,"ariaHidden":53},[66],[28,22741,22743,22746,22786,22789,22792,22795],{"className":22742},[70],[28,22744],{"className":22745,"style":15411},[74],[28,22747,22749,22752],{"className":22748},[79],[28,22750,7634],{"className":22751,"style":7654},[79,80],[28,22753,22755],{"className":22754},[2664],[28,22756,22758,22778],{"className":22757},[2668,2669],[28,22759,22761,22775],{"className":22760},[2673],[28,22762,22764],{"className":22763,"style":11486},[2677],[28,22765,22766,22769],{"style":15432},[28,22767],{"className":22768,"style":2686},[2685],[28,22770,22772],{"className":22771},[2690,2691,2692,2693],[28,22773,6706],{"className":22774},[79,2693],[28,22776,2701],{"className":22777},[2700],[28,22779,22781],{"className":22780},[2673],[28,22782,22784],{"className":22783,"style":2708},[2677],[28,22785],{},[28,22787],{"className":22788,"style":90},[89],[28,22790,17336],{"className":22791},[17246],[28,22793],{"className":22794,"style":90},[89],[28,22796,22798,22801],{"className":22797},[79],[28,22799,7634],{"className":22800,"style":7654},[79,80],[28,22802,22804],{"className":22803},[2664],[28,22805,22807,22827],{"className":22806},[2668,2669],[28,22808,22810,22824],{"className":22809},[2673],[28,22811,22813],{"className":22812,"style":17274},[2677],[28,22814,22815,22818],{"style":15432},[28,22816],{"className":22817,"style":2686},[2685],[28,22819,22821],{"className":22820},[2690,2691,2692,2693],[28,22822,11123],{"className":22823,"style":11155},[79,80,2693],[28,22825,2701],{"className":22826},[2700],[28,22828,22830],{"className":22829},[2673],[28,22831,22833],{"className":22832,"style":2708},[2677],[28,22834],{},[28,22836,22838,22851],{"className":22837},[31],[28,22839,22841],{"className":22840},[35],[37,22842,22843],{"xmlns":39},[41,22844,22845,22849],{},[44,22846,22847],{},[47,22848,6642],{},[59,22850,6642],{"encoding":61},[28,22852,22854],{"className":22853,"ariaHidden":53},[66],[28,22855,22857,22860],{"className":22856},[70],[28,22858],{"className":22859,"style":154},[74],[28,22861,6642],{"className":22862,"style":6663},[79,80]," 也互素。\n",[9797,22865,22866,22867,22949,22950,23076,23077,20056,23231,23259,23260,23535,23536,23727,23728,24004,24005,24008,24009,24232,24233,24588],{},"(注：这是因为在交换幺环中，若 ",[28,22868,22870,22891],{"className":22869},[31],[28,22871,22873],{"className":22872},[35],[37,22874,22875],{"xmlns":39},[41,22876,22877,22889],{},[44,22878,22879,22885,22887],{},[2621,22880,22881,22883],{},[47,22882,7634],{},[47,22884,864],{},[51,22886,54],{"separator":53},[47,22888,6642],{},[59,22890,19697],{"encoding":61},[28,22892,22894],{"className":22893,"ariaHidden":53},[66],[28,22895,22897,22900,22940,22943,22946],{"className":22896},[70],[28,22898],{"className":22899,"style":75},[74],[28,22901,22903,22906],{"className":22902},[79],[28,22904,7634],{"className":22905,"style":7654},[79,80],[28,22907,22909],{"className":22908},[2664],[28,22910,22912,22932],{"className":22911},[2668,2669],[28,22913,22915,22929],{"className":22914},[2673],[28,22916,22918],{"className":22917,"style":14481},[2677],[28,22919,22920,22923],{"style":15432},[28,22921],{"className":22922,"style":2686},[2685],[28,22924,22926],{"className":22925},[2690,2691,2692,2693],[28,22927,864],{"className":22928},[79,80,2693],[28,22930,2701],{"className":22931},[2700],[28,22933,22935],{"className":22934},[2673],[28,22936,22938],{"className":22937,"style":2708},[2677],[28,22939],{},[28,22941,54],{"className":22942},[85],[28,22944],{"className":22945,"style":90},[89],[28,22947,6642],{"className":22948,"style":6663},[79,80]," 互素，则积 ",[28,22951,22953,22978],{"className":22952},[31],[28,22954,22956],{"className":22955},[35],[37,22957,22958],{"xmlns":39},[41,22959,22960,22976],{},[44,22961,22962,22968,22970],{},[2621,22963,22964,22966],{},[47,22965,7634],{},[1731,22967,6706],{},[51,22969,17336],{},[2621,22971,22972,22974],{},[47,22973,7634],{},[47,22975,11123],{},[59,22977,22736],{"encoding":61},[28,22979,22981],{"className":22980,"ariaHidden":53},[66],[28,22982,22984,22987,23027,23030,23033,23036],{"className":22983},[70],[28,22985],{"className":22986,"style":15411},[74],[28,22988,22990,22993],{"className":22989},[79],[28,22991,7634],{"className":22992,"style":7654},[79,80],[28,22994,22996],{"className":22995},[2664],[28,22997,22999,23019],{"className":22998},[2668,2669],[28,23000,23002,23016],{"className":23001},[2673],[28,23003,23005],{"className":23004,"style":11486},[2677],[28,23006,23007,23010],{"style":15432},[28,23008],{"className":23009,"style":2686},[2685],[28,23011,23013],{"className":23012},[2690,2691,2692,2693],[28,23014,6706],{"className":23015},[79,2693],[28,23017,2701],{"className":23018},[2700],[28,23020,23022],{"className":23021},[2673],[28,23023,23025],{"className":23024,"style":2708},[2677],[28,23026],{},[28,23028],{"className":23029,"style":90},[89],[28,23031,17336],{"className":23032},[17246],[28,23034],{"className":23035,"style":90},[89],[28,23037,23039,23042],{"className":23038},[79],[28,23040,7634],{"className":23041,"style":7654},[79,80],[28,23043,23045],{"className":23044},[2664],[28,23046,23048,23068],{"className":23047},[2668,2669],[28,23049,23051,23065],{"className":23050},[2673],[28,23052,23054],{"className":23053,"style":17274},[2677],[28,23055,23056,23059],{"style":15432},[28,23057],{"className":23058,"style":2686},[2685],[28,23060,23062],{"className":23061},[2690,2691,2692,2693],[28,23063,11123],{"className":23064,"style":11155},[79,80,2693],[28,23066,2701],{"className":23067},[2700],[28,23069,23071],{"className":23070},[2673],[28,23072,23074],{"className":23073,"style":2708},[2677],[28,23075],{}," 包含了交集 ",[28,23078,23080,23109],{"className":23079},[31],[28,23081,23083],{"className":23082},[35],[37,23084,23085],{"xmlns":39},[41,23086,23087,23107],{},[44,23088,23089,23095,23097,23099,23101],{},[2621,23090,23091,23093],{},[47,23092,7634],{},[1731,23094,6706],{},[51,23096,10630],{},[51,23098,17336],{},[51,23100,10630],{},[2621,23102,23103,23105],{},[47,23104,7634],{},[47,23106,11123],{},[59,23108,19932],{"encoding":61},[28,23110,23112,23167,23185],{"className":23111,"ariaHidden":53},[66],[28,23113,23115,23118,23158,23161,23164],{"className":23114},[70],[28,23116],{"className":23117,"style":15411},[74],[28,23119,23121,23124],{"className":23120},[79],[28,23122,7634],{"className":23123,"style":7654},[79,80],[28,23125,23127],{"className":23126},[2664],[28,23128,23130,23150],{"className":23129},[2668,2669],[28,23131,23133,23147],{"className":23132},[2673],[28,23134,23136],{"className":23135,"style":11486},[2677],[28,23137,23138,23141],{"style":15432},[28,23139],{"className":23140,"style":2686},[2685],[28,23142,23144],{"className":23143},[2690,2691,2692,2693],[28,23145,6706],{"className":23146},[79,2693],[28,23148,2701],{"className":23149},[2700],[28,23151,23153],{"className":23152},[2673],[28,23154,23156],{"className":23155,"style":2708},[2677],[28,23157],{},[28,23159],{"className":23160,"style":363},[89],[28,23162,10630],{"className":23163},[367],[28,23165],{"className":23166,"style":363},[89],[28,23168,23170,23173,23176,23179,23182],{"className":23169},[70],[28,23171],{"className":23172,"style":19997},[74],[28,23174,17336],{"className":23175},[17246],[28,23177],{"className":23178,"style":363},[89],[28,23180,10630],{"className":23181},[367],[28,23183],{"className":23184,"style":363},[89],[28,23186,23188,23191],{"className":23187},[70],[28,23189],{"className":23190,"style":15411},[74],[28,23192,23194,23197],{"className":23193},[79],[28,23195,7634],{"className":23196,"style":7654},[79,80],[28,23198,23200],{"className":23199},[2664],[28,23201,23203,23223],{"className":23202},[2668,2669],[28,23204,23206,23220],{"className":23205},[2673],[28,23207,23209],{"className":23208,"style":17274},[2677],[28,23210,23211,23214],{"style":15432},[28,23212],{"className":23213,"style":2686},[2685],[28,23215,23217],{"className":23216},[2690,2691,2692,2693],[28,23218,11123],{"className":23219,"style":11155},[79,80,2693],[28,23221,2701],{"className":23222},[2700],[28,23224,23226],{"className":23225},[2673],[28,23227,23229],{"className":23228,"style":2708},[2677],[28,23230],{},[28,23232,23234,23247],{"className":23233},[31],[28,23235,23237],{"className":23236},[35],[37,23238,23239],{"xmlns":39},[41,23240,23241,23245],{},[44,23242,23243],{},[47,23244,6642],{},[59,23246,6642],{"encoding":61},[28,23248,23250],{"className":23249,"ariaHidden":53},[66],[28,23251,23253,23256],{"className":23252},[70],[28,23254],{"className":23255,"style":154},[74],[28,23257,6642],{"className":23258,"style":6663},[79,80]," 的某种组合关系，或者直接利用命题 3.3.5 证明交集互素后，再利用包含关系 ",[28,23261,23263,23309],{"className":23262},[31],[28,23264,23266],{"className":23265},[35],[37,23267,23268],{"xmlns":39},[41,23269,23270,23306],{},[44,23271,23272,23278,23280,23286,23288,23294,23296,23298,23300],{},[2621,23273,23274,23276],{},[47,23275,7634],{},[1731,23277,6706],{},[51,23279,17336],{},[2621,23281,23282,23284],{},[47,23283,7634],{},[47,23285,11123],{},[51,23287,11216],{},[2621,23289,23290,23292],{},[47,23291,7634],{},[1731,23293,6706],{},[51,23295,10630],{},[51,23297,17336],{},[51,23299,10630],{},[2621,23301,23302,23304],{},[47,23303,7634],{},[47,23305,11123],{},[59,23307,23308],{"encoding":61},"I_1 \\cdots I_k \\subseteq I_1 \\cap \\dots \\cap I_k",[28,23310,23312,23416,23471,23489],{"className":23311,"ariaHidden":53},[66],[28,23313,23315,23318,23358,23361,23364,23367,23407,23410,23413],{"className":23314},[70],[28,23316],{"className":23317,"style":15411},[74],[28,23319,23321,23324],{"className":23320},[79],[28,23322,7634],{"className":23323,"style":7654},[79,80],[28,23325,23327],{"className":23326},[2664],[28,23328,23330,23350],{"className":23329},[2668,2669],[28,23331,23333,23347],{"className":23332},[2673],[28,23334,23336],{"className":23335,"style":11486},[2677],[28,23337,23338,23341],{"style":15432},[28,23339],{"className":23340,"style":2686},[2685],[28,23342,23344],{"className":23343},[2690,2691,2692,2693],[28,23345,6706],{"className":23346},[79,2693],[28,23348,2701],{"className":23349},[2700],[28,23351,23353],{"className":23352},[2673],[28,23354,23356],{"className":23355,"style":2708},[2677],[28,23357],{},[28,23359],{"className":23360,"style":90},[89],[28,23362,17336],{"className":23363},[17246],[28,23365],{"className":23366,"style":90},[89],[28,23368,23370,23373],{"className":23369},[79],[28,23371,7634],{"className":23372,"style":7654},[79,80],[28,23374,23376],{"className":23375},[2664],[28,23377,23379,23399],{"className":23378},[2668,2669],[28,23380,23382,23396],{"className":23381},[2673],[28,23383,23385],{"className":23384,"style":17274},[2677],[28,23386,23387,23390],{"style":15432},[28,23388],{"className":23389,"style":2686},[2685],[28,23391,23393],{"className":23392},[2690,2691,2692,2693],[28,23394,11123],{"className":23395,"style":11155},[79,80,2693],[28,23397,2701],{"className":23398},[2700],[28,23400,23402],{"className":23401},[2673],[28,23403,23405],{"className":23404,"style":2708},[2677],[28,23406],{},[28,23408],{"className":23409,"style":140},[89],[28,23411,11216],{"className":23412},[144],[28,23414],{"className":23415,"style":140},[89],[28,23417,23419,23422,23462,23465,23468],{"className":23418},[70],[28,23420],{"className":23421,"style":15411},[74],[28,23423,23425,23428],{"className":23424},[79],[28,23426,7634],{"className":23427,"style":7654},[79,80],[28,23429,23431],{"className":23430},[2664],[28,23432,23434,23454],{"className":23433},[2668,2669],[28,23435,23437,23451],{"className":23436},[2673],[28,23438,23440],{"className":23439,"style":11486},[2677],[28,23441,23442,23445],{"style":15432},[28,23443],{"className":23444,"style":2686},[2685],[28,23446,23448],{"className":23447},[2690,2691,2692,2693],[28,23449,6706],{"className":23450},[79,2693],[28,23452,2701],{"className":23453},[2700],[28,23455,23457],{"className":23456},[2673],[28,23458,23460],{"className":23459,"style":2708},[2677],[28,23461],{},[28,23463],{"className":23464,"style":363},[89],[28,23466,10630],{"className":23467},[367],[28,23469],{"className":23470,"style":363},[89],[28,23472,23474,23477,23480,23483,23486],{"className":23473},[70],[28,23475],{"className":23476,"style":19997},[74],[28,23478,17336],{"className":23479},[17246],[28,23481],{"className":23482,"style":363},[89],[28,23484,10630],{"className":23485},[367],[28,23487],{"className":23488,"style":363},[89],[28,23490,23492,23495],{"className":23491},[70],[28,23493],{"className":23494,"style":15411},[74],[28,23496,23498,23501],{"className":23497},[79],[28,23499,7634],{"className":23500,"style":7654},[79,80],[28,23502,23504],{"className":23503},[2664],[28,23505,23507,23527],{"className":23506},[2668,2669],[28,23508,23510,23524],{"className":23509},[2673],[28,23511,23513],{"className":23512,"style":17274},[2677],[28,23514,23515,23518],{"style":15432},[28,23516],{"className":23517,"style":2686},[2685],[28,23519,23521],{"className":23520},[2690,2691,2692,2693],[28,23522,11123],{"className":23523,"style":11155},[79,80,2693],[28,23525,2701],{"className":23526},[2700],[28,23528,23530],{"className":23529},[2673],[28,23531,23533],{"className":23532,"style":2708},[2677],[28,23534],{}," 并不足以直接推出互素，这里通常需要重新利用 ",[28,23537,23539,23581],{"className":23538},[31],[28,23540,23542],{"className":23541},[35],[37,23543,23544],{"xmlns":39},[41,23545,23546,23578],{},[44,23547,23548,23550,23556,23558,23560,23562,23564,23566,23572,23574,23576],{},[51,23549,269],{"stretchy":268},[2621,23551,23552,23554],{},[47,23553,7634],{},[1731,23555,6706],{},[51,23557,274],{},[47,23559,6642],{},[51,23561,279],{"stretchy":268},[51,23563,17336],{},[51,23565,269],{"stretchy":268},[2621,23567,23568,23570],{},[47,23569,7634],{},[47,23571,11123],{},[51,23573,274],{},[47,23575,6642],{},[51,23577,279],{"stretchy":268},[59,23579,23580],{"encoding":61},"(I_1+J)\\cdots(I_k+J)",[28,23582,23584,23642,23715],{"className":23583,"ariaHidden":53},[66],[28,23585,23587,23590,23593,23633,23636,23639],{"className":23586},[70],[28,23588],{"className":23589,"style":349},[74],[28,23591,269],{"className":23592},[356],[28,23594,23596,23599],{"className":23595},[79],[28,23597,7634],{"className":23598,"style":7654},[79,80],[28,23600,23602],{"className":23601},[2664],[28,23603,23605,23625],{"className":23604},[2668,2669],[28,23606,23608,23622],{"className":23607},[2673],[28,23609,23611],{"className":23610,"style":11486},[2677],[28,23612,23613,23616],{"style":15432},[28,23614],{"className":23615,"style":2686},[2685],[28,23617,23619],{"className":23618},[2690,2691,2692,2693],[28,23620,6706],{"className":23621},[79,2693],[28,23623,2701],{"className":23624},[2700],[28,23626,23628],{"className":23627},[2673],[28,23629,23631],{"className":23630,"style":2708},[2677],[28,23632],{},[28,23634],{"className":23635,"style":363},[89],[28,23637,274],{"className":23638},[367],[28,23640],{"className":23641,"style":363},[89],[28,23643,23645,23648,23651,23654,23657,23660,23663,23666,23706,23709,23712],{"className":23644},[70],[28,23646],{"className":23647,"style":349},[74],[28,23649,6642],{"className":23650,"style":6663},[79,80],[28,23652,279],{"className":23653},[383],[28,23655],{"className":23656,"style":90},[89],[28,23658,17336],{"className":23659},[17246],[28,23661],{"className":23662,"style":90},[89],[28,23664,269],{"className":23665},[356],[28,23667,23669,23672],{"className":23668},[79],[28,23670,7634],{"className":23671,"style":7654},[79,80],[28,23673,23675],{"className":23674},[2664],[28,23676,23678,23698],{"className":23677},[2668,2669],[28,23679,23681,23695],{"className":23680},[2673],[28,23682,23684],{"className":23683,"style":17274},[2677],[28,23685,23686,23689],{"style":15432},[28,23687],{"className":23688,"style":2686},[2685],[28,23690,23692],{"className":23691},[2690,2691,2692,2693],[28,23693,11123],{"className":23694,"style":11155},[79,80,2693],[28,23696,2701],{"className":23697},[2700],[28,23699,23701],{"className":23700},[2673],[28,23702,23704],{"className":23703,"style":2708},[2677],[28,23705],{},[28,23707],{"className":23708,"style":363},[89],[28,23710,274],{"className":23711},[367],[28,23713],{"className":23714,"style":363},[89],[28,23716,23718,23721,23724],{"className":23717},[70],[28,23719],{"className":23720,"style":349},[74],[28,23722,6642],{"className":23723,"style":6663},[79,80],[28,23725,279],{"className":23726},[383]," 的展开式或者利用根理想性质。但在本讲义的逻辑流中，通常是利用 ",[28,23729,23731,23778],{"className":23730},[31],[28,23732,23734],{"className":23733},[35],[37,23735,23736],{"xmlns":39},[41,23737,23738,23775],{},[44,23739,23740,23746,23748,23750,23752,23758,23761,23767,23769],{},[2621,23741,23742,23744],{},[47,23743,7634],{},[1731,23745,6706],{},[51,23747,10630],{},[51,23749,17336],{},[51,23751,10630],{},[2621,23753,23754,23756],{},[47,23755,7634],{},[47,23757,11123],{},[51,23759,23760],{},"⊇",[2621,23762,23763,23765],{},[47,23764,7634],{},[1731,23766,6706],{},[51,23768,17336],{},[2621,23770,23771,23773],{},[47,23772,7634],{},[47,23774,11123],{},[59,23776,23777],{"encoding":61},"I_1 \\cap \\dots \\cap I_k \\supseteq I_1 \\cdots I_k",[28,23779,23781,23836,23854,23909],{"className":23780,"ariaHidden":53},[66],[28,23782,23784,23787,23827,23830,23833],{"className":23783},[70],[28,23785],{"className":23786,"style":15411},[74],[28,23788,23790,23793],{"className":23789},[79],[28,23791,7634],{"className":23792,"style":7654},[79,80],[28,23794,23796],{"className":23795},[2664],[28,23797,23799,23819],{"className":23798},[2668,2669],[28,23800,23802,23816],{"className":23801},[2673],[28,23803,23805],{"className":23804,"style":11486},[2677],[28,23806,23807,23810],{"style":15432},[28,23808],{"className":23809,"style":2686},[2685],[28,23811,23813],{"className":23812},[2690,2691,2692,2693],[28,23814,6706],{"className":23815},[79,2693],[28,23817,2701],{"className":23818},[2700],[28,23820,23822],{"className":23821},[2673],[28,23823,23825],{"className":23824,"style":2708},[2677],[28,23826],{},[28,23828],{"className":23829,"style":363},[89],[28,23831,10630],{"className":23832},[367],[28,23834],{"className":23835,"style":363},[89],[28,23837,23839,23842,23845,23848,23851],{"className":23838},[70],[28,23840],{"className":23841,"style":19997},[74],[28,23843,17336],{"className":23844},[17246],[28,23846],{"className":23847,"style":363},[89],[28,23849,10630],{"className":23850},[367],[28,23852],{"className":23853,"style":363},[89],[28,23855,23857,23860,23900,23903,23906],{"className":23856},[70],[28,23858],{"className":23859,"style":15411},[74],[28,23861,23863,23866],{"className":23862},[79],[28,23864,7634],{"className":23865,"style":7654},[79,80],[28,23867,23869],{"className":23868},[2664],[28,23870,23872,23892],{"className":23871},[2668,2669],[28,23873,23875,23889],{"className":23874},[2673],[28,23876,23878],{"className":23877,"style":17274},[2677],[28,23879,23880,23883],{"style":15432},[28,23881],{"className":23882,"style":2686},[2685],[28,23884,23886],{"className":23885},[2690,2691,2692,2693],[28,23887,11123],{"className":23888,"style":11155},[79,80,2693],[28,23890,2701],{"className":23891},[2700],[28,23893,23895],{"className":23894},[2673],[28,23896,23898],{"className":23897,"style":2708},[2677],[28,23899],{},[28,23901],{"className":23902,"style":140},[89],[28,23904,23760],{"className":23905},[144],[28,23907],{"className":23908,"style":140},[89],[28,23910,23912,23915,23955,23958,23961,23964],{"className":23911},[70],[28,23913],{"className":23914,"style":15411},[74],[28,23916,23918,23921],{"className":23917},[79],[28,23919,7634],{"className":23920,"style":7654},[79,80],[28,23922,23924],{"className":23923},[2664],[28,23925,23927,23947],{"className":23926},[2668,2669],[28,23928,23930,23944],{"className":23929},[2673],[28,23931,23933],{"className":23932,"style":11486},[2677],[28,23934,23935,23938],{"style":15432},[28,23936],{"className":23937,"style":2686},[2685],[28,23939,23941],{"className":23940},[2690,2691,2692,2693],[28,23942,6706],{"className":23943},[79,2693],[28,23945,2701],{"className":23946},[2700],[28,23948,23950],{"className":23949},[2673],[28,23951,23953],{"className":23952,"style":2708},[2677],[28,23954],{},[28,23956],{"className":23957,"style":90},[89],[28,23959,17336],{"className":23960},[17246],[28,23962],{"className":23963,"style":90},[89],[28,23965,23967,23970],{"className":23966},[79],[28,23968,7634],{"className":23969,"style":7654},[79,80],[28,23971,23973],{"className":23972},[2664],[28,23974,23976,23996],{"className":23975},[2668,2669],[28,23977,23979,23993],{"className":23978},[2673],[28,23980,23982],{"className":23981,"style":17274},[2677],[28,23983,23984,23987],{"style":15432},[28,23985],{"className":23986,"style":2686},[2685],[28,23988,23990],{"className":23989},[2690,2691,2692,2693],[28,23991,11123],{"className":23992,"style":11155},[79,80,2693],[28,23994,2701],{"className":23995},[2700],[28,23997,23999],{"className":23998},[2673],[28,24000,24002],{"className":24001,"style":2708},[2677],[28,24003],{},"，如果交集与 J 互素，我们需要更强的条件。",[23,24006,24007],{},"更正","：实际上，推论通常是由命题 3.3.5 结合 ",[28,24010,24012,24059],{"className":24011},[31],[28,24013,24015],{"className":24014},[35],[37,24016,24017],{"xmlns":39},[41,24018,24019,24056],{},[44,24020,24021,24023,24025,24028,24030,24036,24038,24040,24042,24044,24046,24052,24054],{},[47,24022,49],{},[51,24024,282],{},[51,24026,24027],{},"∏",[51,24029,269],{"stretchy":268},[2621,24031,24032,24034],{},[47,24033,7634],{},[47,24035,864],{},[51,24037,274],{},[47,24039,6642],{},[51,24041,279],{"stretchy":268},[51,24043,11216],{},[51,24045,24027],{},[2621,24047,24048,24050],{},[47,24049,7634],{},[47,24051,864],{},[51,24053,274],{},[47,24055,6642],{},[59,24057,24058],{"encoding":61},"R = \\prod (I_s+J) \\subseteq \\prod I_s + J",[28,24060,24062,24080,24141,24162,24223],{"className":24061,"ariaHidden":53},[66],[28,24063,24065,24068,24071,24074,24077],{"className":24064},[70],[28,24066],{"className":24067,"style":154},[74],[28,24069,49],{"className":24070,"style":81},[79,80],[28,24072],{"className":24073,"style":140},[89],[28,24075,282],{"className":24076},[144],[28,24078],{"className":24079,"style":140},[89],[28,24081,24083,24086,24089,24092,24132,24135,24138],{"className":24082},[70],[28,24084],{"className":24085,"style":349},[74],[28,24087,24027],{"className":24088,"style":17723},[1385,17721,17722],[28,24090,269],{"className":24091},[356],[28,24093,24095,24098],{"className":24094},[79],[28,24096,7634],{"className":24097,"style":7654},[79,80],[28,24099,24101],{"className":24100},[2664],[28,24102,24104,24124],{"className":24103},[2668,2669],[28,24105,24107,24121],{"className":24106},[2673],[28,24108,24110],{"className":24109,"style":14481},[2677],[28,24111,24112,24115],{"style":15432},[28,24113],{"className":24114,"style":2686},[2685],[28,24116,24118],{"className":24117},[2690,2691,2692,2693],[28,24119,864],{"className":24120},[79,80,2693],[28,24122,2701],{"className":24123},[2700],[28,24125,24127],{"className":24126},[2673],[28,24128,24130],{"className":24129,"style":2708},[2677],[28,24131],{},[28,24133],{"className":24134,"style":363},[89],[28,24136,274],{"className":24137},[367],[28,24139],{"className":24140,"style":363},[89],[28,24142,24144,24147,24150,24153,24156,24159],{"className":24143},[70],[28,24145],{"className":24146,"style":349},[74],[28,24148,6642],{"className":24149,"style":6663},[79,80],[28,24151,279],{"className":24152},[383],[28,24154],{"className":24155,"style":140},[89],[28,24157,11216],{"className":24158},[144],[28,24160],{"className":24161,"style":140},[89],[28,24163,24165,24168,24171,24174,24214,24217,24220],{"className":24164},[70],[28,24166],{"className":24167,"style":349},[74],[28,24169,24027],{"className":24170,"style":17723},[1385,17721,17722],[28,24172],{"className":24173,"style":90},[89],[28,24175,24177,24180],{"className":24176},[79],[28,24178,7634],{"className":24179,"style":7654},[79,80],[28,24181,24183],{"className":24182},[2664],[28,24184,24186,24206],{"className":24185},[2668,2669],[28,24187,24189,24203],{"className":24188},[2673],[28,24190,24192],{"className":24191,"style":14481},[2677],[28,24193,24194,24197],{"style":15432},[28,24195],{"className":24196,"style":2686},[2685],[28,24198,24200],{"className":24199},[2690,2691,2692,2693],[28,24201,864],{"className":24202},[79,80,2693],[28,24204,2701],{"className":24205},[2700],[28,24207,24209],{"className":24208},[2673],[28,24210,24212],{"className":24211,"style":2708},[2677],[28,24213],{},[28,24215],{"className":24216,"style":363},[89],[28,24218,274],{"className":24219},[367],[28,24221],{"className":24222,"style":363},[89],[28,24224,24226,24229],{"className":24225},[70],[28,24227],{"className":24228,"style":154},[74],[28,24230,6642],{"className":24231,"style":6663},[79,80]," 得到的。即 ",[28,24234,24236,24302],{"className":24235},[31],[28,24237,24239],{"className":24238},[35],[37,24240,24241],{"xmlns":39},[41,24242,24243,24299],{},[44,24244,24245,24247,24249,24251,24257,24259,24261,24263,24265,24267,24273,24275,24277,24279,24281,24287,24289,24295,24297],{},[47,24246,49],{},[51,24248,282],{},[51,24250,269],{"stretchy":268},[2621,24252,24253,24255],{},[47,24254,7634],{},[1731,24256,6706],{},[51,24258,274],{},[47,24260,6642],{},[51,24262,279],{"stretchy":268},[51,24264,17172],{},[51,24266,269],{"stretchy":268},[2621,24268,24269,24271],{},[47,24270,7634],{},[47,24272,11123],{},[51,24274,274],{},[47,24276,6642],{},[51,24278,279],{"stretchy":268},[51,24280,11216],{},[2621,24282,24283,24285],{},[47,24284,7634],{},[1731,24286,6706],{},[51,24288,17172],{},[2621,24290,24291,24293],{},[47,24292,7634],{},[47,24294,11123],{},[51,24296,274],{},[47,24298,6642],{},[59,24300,24301],{"encoding":61},"R = (I_1+J)\\dots(I_k+J) \\subseteq I_1\\dots I_k + J",[28,24303,24305,24323,24381,24454,24475,24579],{"className":24304,"ariaHidden":53},[66],[28,24306,24308,24311,24314,24317,24320],{"className":24307},[70],[28,24309],{"className":24310,"style":154},[74],[28,24312,49],{"className":24313,"style":81},[79,80],[28,24315],{"className":24316,"style":140},[89],[28,24318,282],{"className":24319},[144],[28,24321],{"className":24322,"style":140},[89],[28,24324,24326,24329,24332,24372,24375,24378],{"className":24325},[70],[28,24327],{"className":24328,"style":349},[74],[28,24330,269],{"className":24331},[356],[28,24333,24335,24338],{"className":24334},[79],[28,24336,7634],{"className":24337,"style":7654},[79,80],[28,24339,24341],{"className":24340},[2664],[28,24342,24344,24364],{"className":24343},[2668,2669],[28,24345,24347,24361],{"className":24346},[2673],[28,24348,24350],{"className":24349,"style":11486},[2677],[28,24351,24352,24355],{"style":15432},[28,24353],{"className":24354,"style":2686},[2685],[28,24356,24358],{"className":24357},[2690,2691,2692,2693],[28,24359,6706],{"className":24360},[79,2693],[28,24362,2701],{"className":24363},[2700],[28,24365,24367],{"className":24366},[2673],[28,24368,24370],{"className":24369,"style":2708},[2677],[28,24371],{},[28,24373],{"className":24374,"style":363},[89],[28,24376,274],{"className":24377},[367],[28,24379],{"className":24380,"style":363},[89],[28,24382,24384,24387,24390,24393,24396,24399,24402,24405,24445,24448,24451],{"className":24383},[70],[28,24385],{"className":24386,"style":349},[74],[28,24388,6642],{"className":24389,"style":6663},[79,80],[28,24391,279],{"className":24392},[383],[28,24394],{"className":24395,"style":90},[89],[28,24397,17172],{"className":24398},[17246],[28,24400],{"className":24401,"style":90},[89],[28,24403,269],{"className":24404},[356],[28,24406,24408,24411],{"className":24407},[79],[28,24409,7634],{"className":24410,"style":7654},[79,80],[28,24412,24414],{"className":24413},[2664],[28,24415,24417,24437],{"className":24416},[2668,2669],[28,24418,24420,24434],{"className":24419},[2673],[28,24421,24423],{"className":24422,"style":17274},[2677],[28,24424,24425,24428],{"style":15432},[28,24426],{"className":24427,"style":2686},[2685],[28,24429,24431],{"className":24430},[2690,2691,2692,2693],[28,24432,11123],{"className":24433,"style":11155},[79,80,2693],[28,24435,2701],{"className":24436},[2700],[28,24438,24440],{"className":24439},[2673],[28,24441,24443],{"className":24442,"style":2708},[2677],[28,24444],{},[28,24446],{"className":24447,"style":363},[89],[28,24449,274],{"className":24450},[367],[28,24452],{"className":24453,"style":363},[89],[28,24455,24457,24460,24463,24466,24469,24472],{"className":24456},[70],[28,24458],{"className":24459,"style":349},[74],[28,24461,6642],{"className":24462,"style":6663},[79,80],[28,24464,279],{"className":24465},[383],[28,24467],{"className":24468,"style":140},[89],[28,24470,11216],{"className":24471},[144],[28,24473],{"className":24474,"style":140},[89],[28,24476,24478,24481,24521,24524,24527,24530,24570,24573,24576],{"className":24477},[70],[28,24479],{"className":24480,"style":15411},[74],[28,24482,24484,24487],{"className":24483},[79],[28,24485,7634],{"className":24486,"style":7654},[79,80],[28,24488,24490],{"className":24489},[2664],[28,24491,24493,24513],{"className":24492},[2668,2669],[28,24494,24496,24510],{"className":24495},[2673],[28,24497,24499],{"className":24498,"style":11486},[2677],[28,24500,24501,24504],{"style":15432},[28,24502],{"className":24503,"style":2686},[2685],[28,24505,24507],{"className":24506},[2690,2691,2692,2693],[28,24508,6706],{"className":24509},[79,2693],[28,24511,2701],{"className":24512},[2700],[28,24514,24516],{"className":24515},[2673],[28,24517,24519],{"className":24518,"style":2708},[2677],[28,24520],{},[28,24522],{"className":24523,"style":90},[89],[28,24525,17172],{"className":24526},[17246],[28,24528],{"className":24529,"style":90},[89],[28,24531,24533,24536],{"className":24532},[79],[28,24534,7634],{"className":24535,"style":7654},[79,80],[28,24537,24539],{"className":24538},[2664],[28,24540,24542,24562],{"className":24541},[2668,2669],[28,24543,24545,24559],{"className":24544},[2673],[28,24546,24548],{"className":24547,"style":17274},[2677],[28,24549,24550,24553],{"style":15432},[28,24551],{"className":24552,"style":2686},[2685],[28,24554,24556],{"className":24555},[2690,2691,2692,2693],[28,24557,11123],{"className":24558,"style":11155},[79,80,2693],[28,24560,2701],{"className":24561},[2700],[28,24563,24565],{"className":24564},[2673],[28,24566,24568],{"className":24567,"style":2708},[2677],[28,24569],{},[28,24571],{"className":24572,"style":363},[89],[28,24574,274],{"className":24575},[367],[28,24577],{"className":24578,"style":363},[89],[28,24580,24582,24585],{"className":24581},[70],[28,24583],{"className":24584,"style":154},[74],[28,24586,6642],{"className":24587,"style":6663},[79,80],", 从而得证。)",{"title":24590,"searchDepth":24591,"depth":24591,"links":24592},"",2,[24593,24595,24596,24597,24598],{"id":17,"depth":24594,"text":18},3,{"id":1990,"depth":24594,"text":1991},{"id":7613,"depth":24594,"text":7614},{"id":14375,"depth":24594,"text":14376},{"id":15565,"depth":24594,"text":15566},"md",{"order":24601},6,true,"\u002Fsource\u002Fmath\u002Fabstract_algebra\u002Fringhomomorphism",{"title":5,"description":24590},"source\u002Fmath\u002Fabstract_algebra\u002Fringhomomorphism","IqswxktgDKTOmFTcCPHBq7vlhvt2XwaLUCUUbQ-STkA",null,1784032894293]