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1、PolynomialIdentitiesinRingTheoryThisisavolumeinPUREANDAPPLIEDMATHEMATICSASeriesofMonographsandTextbooksEditors:SAMUELEILENBERGANDHYMANBASSAlistofrecenttitlesinthisseriesappearsattheendofthisvolume.PolynomialIdentitiesinRingTheoryLouisHaleRowenDepartmentofMathematicsandComputerScienceBar-ll
2、anUniversityRamat-Can.Israel1980ACADEMICPRESSASubsidiaryofHarcourtBraceJovanovich,PublishersNewYorkLondonTorontoSydneySanFranciscoCOPYRIGHT@1980,BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTMISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPH
3、OTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITINGFROMTHEPUBLISHER.ACADEMICPRESS,INC.111FifthAvenue,NewYork,NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS.INC.(LONDON)LTD.14/18OvalRoad.LondonNW17DXLibraryofCongressCataloginginPublicationDataRow
4、en,LouisHalle.Polynomialidentitiesinringtheory.Bibliography:p.1.Polynomialrings.I.Title.QA251.3.R6851.Y.479-12923ISBN0-12-599850-3AMS(MOS)ClassificationNumbers:Primary16A28,16A38,16A40Secondary16A46,16A48PRINTEDINTHEUNITEDSTATESOFAMERICA80818283987654321ThisbookiswrittentohonorthememoryofS
5、eymourM.Rowen.September3,1917-October7,1976ThisPageIntentionallyLeftBlankCONTENTS...PREFACEx111PREREQUISITESxixCHAPTER1TheStructureofPI-Rings1.1.BasicConceptsandExamples2TheFreeMonoidA(X)2TheFreeAlgebra$X}3Identities4Multilinearization6NormalPolynomials7ExamplesofPI-Rings9I.2.FactsaboutNo
6、rmalPolynomialsIICapelliPolynomialsandStandardPolynomials121.3.MatrixAlgebras14MatricesandAlgebrasofEndomorphisms14.TheTrace15TheAlgebra&{Y}ofGenericMatrices15ModifringtheAlgebraofGenericMatrices16TheGeneralCayley-HamiltonTheoremandNewton’sFormulas18TheRegularRepresentation19NilpotentSubse
7、ts191.4.IdentitiesandCentralPolynomialsforMatrixAlgebras,andTheirApplicationstoArbitraryPI-Algebras20TheAmitsur-LevitzkiTheorems21TheRoieoftheCapelliPolynomial23CentralPolynomials,Featuringg,24Propertiesojnz-Normal.CentralPolynomialsofArbitraryRings21LinearDep
