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1、ABSTRACTALGEBRAABSTRACTALGEBRAThirdEditionI.N.HersteinLateProfessorofMathematicsUniversityofChicagoPRENTICE-HALL,UpperSaddleRiver,NewJersey07458LibraryofCongressCataloginginPublicationDataHerstein,I.N.AbstractalgebraII.N.Herstein.-3rded.p.cm.Includesindex.lSBN0-13-374562-7(alk.paper)1.Algebra,
2、Abstract.I.TitleQA162.H47199595-21470512l.02--dc20CIPAcquisitionEditor:GeorgeLobellEditor-in-Chief:JeromeGrantProductionEditor:ElaineWetterauiUniversityGraphics,Inc.ArtDirector:JayneConteCoverDesigner:BruceKenselaarCoverPhotograph:CharnleyResidence,entryway.PhotobyONickMerricklHedrich-Blessing
3、ManufacturingBuyer:AlanFischerMarketingManager:FrankNicolazzoO1996Prentice-Hall,Inc.Simon&SchusterIAViacomCompanyUpperSaddleRiver,NewJersey07458Allrightsresewed.Nopartofthisbookmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublisher.EarliereditionsO1986and1990.Printedi
4、ntheUnitedStatesofAmerica1098765432ISBN0-13-374562-7Prentice-HallInternational(UK)Limited,LondonPrentice-HallofAustraliaPty.Limited,SydneyPrentice-HallCanadaInc.,TorontoPrentice-HallHispanoamericana,S.A.,MexicoPrentice-HallofIndiaPrivateLimited,NewDelhiPrentice-HallofJapan,Inc.,TokyoSimon&Schu
5、sterAsiaPte.Ltd.,SingaporeEditoraPrentice-HalldoBrasil,Ltda..RiodeJaneiroCONTENTSPrefaceix1ThingsFamiliarandlessFamiliar11AFewPreliminaryRemarks12SetTheory33Mappings84A(S)(TheSetof1-1MappingsofSontoItself)165TheIntegers216MathematicalInduction297ComplexNumbers322Groups40DefinitionsandExampleso
6、fGroups40SomeSimpleRemarks48Subgroups51Lagrange'sTheorem56HomomorphismsandNormalSubgroups66FactorGroups77TheHomomorphismTheorems84Cauchy'sTheorem88DirectProducts92FiniteAbelianGroups(Optional)96ConjugacyandSylow'sTheorem(Optional)101viiiContents3TheSymmetricGroup1081Preliminaries1082CycleDecom
7、position1113OddandEvenPermutations1194RingTheory1251DefinitionsandExamples1252SomeSimpleResults1373Ideals,Homomorphisms,andQuotientRings1394MaximalIdeals1485PolynomialRings1516PolynomialsovertheRationals1667FieldofQuotientsofanIntegralD
