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2004-11
版次: 1
ISBN: 9787506271844
定价: 126.00
装帧: 精装
开本: 24开
纸张: 胶版纸
页数: 914页
分类: 自然科学
127人买过
  •   AsIseeit,thegraduatecourseinalgebramustprimarilypreparestudentstohandlethealgebrawhichtheywillmeetinallofmathematics:topology,partialdifferentialequations,differentialgeometry,algebraicgeometry,analysis,andrepresentationtheory,nottospeakofalgebraitselfandalgebraicnumbertheorywithallitsramifications.HenceIhaveinsertedthroughoutreferencestopapersandbookswhichhaveappearedduringthelastdecades,toindicatesomeofthedirectionsinwhichthealgebraicfoundationsprovidedbythisbookareused;Ihaveaccompaniedthesereferenceswithsomemotivatingcomments,toexplainhowthetopicsofthepresentbookfitintothemathematicsthatistocomesubsequentlyinvariousfields;andIhavealsomentionedsomeunsolvedproblemsofmathematicsinalgebraandnumbertheory.Theabcconjectureisperhapsthemostspectacularofthese. PartOneTheBasicObjectsofAlgebra
    Chapter1Groups
    1.Monoids
    2.Groups
    3.Normalsubgroups
    4.Cyclicgroups
    5.Operationsofagrouponaset
    6.Sylowsubgroups
    7.Directsumsandfreeabeliangroups
    8.Finitelygeneratedabeliangroups
    9.Thedualgroup
    10.Inverselimitandcompletion
    11.Categoriesandfunctors
    12.Freegroups
    Chapter2Rings
    1.Ringsandhomomorphisms
    2.Commutativerings
    3.Polynomialsandgrouprings
    4.Localization
    5.Principalandfactorialrings
    Chapter3Modules
    Chapter4Polynomlals
    PartTwoAlgebraicEquations
    Chapter5AlgebralcExtensions
    Chapter6GaloisTheory
    Chapter7ExtensionsofRings
    Chapter8TranscendentalExtensions
    Chapter9AlgebraicSpaces
    Chapter10NoetherialRingsandModules
    Chapter11RealFields
    Chapter12AbsoluteValues
    PartThreeLiearAlebarandReqresentations
    Chapter13MatricesandLinearMaps
    Chapter14RepresentatlonofOneEndomorphism
    Chapter15StructureofBilinearForms
    Chapter16TheTensorProduct
    Chapter17Smisimplicity
    Chapter18RepresentationsofFiniteGroups
    Chapter19TheAlternatingProduct
    PartFourHomologicalAlgebra
    Chapter20GeneralHomologyTheory
    Chapter21FiniteFreeResolutions
    Appendix1TheTranscendenceofeand
    Appendix2SomeSetTheory
    Bibliography
    Index
  • 内容简介:
      AsIseeit,thegraduatecourseinalgebramustprimarilypreparestudentstohandlethealgebrawhichtheywillmeetinallofmathematics:topology,partialdifferentialequations,differentialgeometry,algebraicgeometry,analysis,andrepresentationtheory,nottospeakofalgebraitselfandalgebraicnumbertheorywithallitsramifications.HenceIhaveinsertedthroughoutreferencestopapersandbookswhichhaveappearedduringthelastdecades,toindicatesomeofthedirectionsinwhichthealgebraicfoundationsprovidedbythisbookareused;Ihaveaccompaniedthesereferenceswithsomemotivatingcomments,toexplainhowthetopicsofthepresentbookfitintothemathematicsthatistocomesubsequentlyinvariousfields;andIhavealsomentionedsomeunsolvedproblemsofmathematicsinalgebraandnumbertheory.Theabcconjectureisperhapsthemostspectacularofthese.
  • 目录:
    PartOneTheBasicObjectsofAlgebra
    Chapter1Groups
    1.Monoids
    2.Groups
    3.Normalsubgroups
    4.Cyclicgroups
    5.Operationsofagrouponaset
    6.Sylowsubgroups
    7.Directsumsandfreeabeliangroups
    8.Finitelygeneratedabeliangroups
    9.Thedualgroup
    10.Inverselimitandcompletion
    11.Categoriesandfunctors
    12.Freegroups
    Chapter2Rings
    1.Ringsandhomomorphisms
    2.Commutativerings
    3.Polynomialsandgrouprings
    4.Localization
    5.Principalandfactorialrings
    Chapter3Modules
    Chapter4Polynomlals
    PartTwoAlgebraicEquations
    Chapter5AlgebralcExtensions
    Chapter6GaloisTheory
    Chapter7ExtensionsofRings
    Chapter8TranscendentalExtensions
    Chapter9AlgebraicSpaces
    Chapter10NoetherialRingsandModules
    Chapter11RealFields
    Chapter12AbsoluteValues
    PartThreeLiearAlebarandReqresentations
    Chapter13MatricesandLinearMaps
    Chapter14RepresentatlonofOneEndomorphism
    Chapter15StructureofBilinearForms
    Chapter16TheTensorProduct
    Chapter17Smisimplicity
    Chapter18RepresentationsofFiniteGroups
    Chapter19TheAlternatingProduct
    PartFourHomologicalAlgebra
    Chapter20GeneralHomologyTheory
    Chapter21FiniteFreeResolutions
    Appendix1TheTranscendenceofeand
    Appendix2SomeSetTheory
    Bibliography
    Index
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