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同调代数

同调代数
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作者: （Henri Cartan） 著 , （Henri Cartan） 著
出版社: 世界图书出版公司
2011-07
版次: 1
ISBN: 9787510037474
定价: 59.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 390页
正文语种: 英语
分类: 自然科学
2 张插图图片
55人买过
  • Duringthelastdecadethemethodsofalgebraictopologyhaveinvadedextensivelythedomainofpurealgebra,andinitiatedanumberofinternalrevolutions.Thepurposeofthisbookistopresentaunifiedaccountofthesedevelopmentsandtolaythefoundationsofafull-fledgedtheory.
    Theinvasionofalgebrahasoccurredonthreefrontsthroughtheconstructionofcohomologytheoriesforgroups,Liealgebras,andassociativealgebras.Thethreesubjectshavebeengivenindependentbutparalleldevelopments.Wepresenthereinasinglecohomology（andalsoahomology）theorywhichembodiesallthree；eachisobtainedfromitbyasuitablespecialization. Preface
    Chapter1.RingsandModules
    1.Preliminaries
    2.Projectivemodules
    3.Injectivemodules
    4.Semi-simplerings
    5.Hereditaryrings
    6.Semi-hereditaryrings
    7.Noetherianrings
    Exercises

    Chapter2.AdditiveFunctors
    I.Definitions
    2.Examples
    3.Operators
    4.Preservationofexactness
    5.Compositefunctors
    6.Changeofrings
    Exercises

    Chapter3.Satellites
    1.Definitionofsatellites
    2.Connectinghomomorphisms
    3.Halfexactfunctors
    4.Connectedsequenceoffunctors
    5.Axiomaticdescriptionofsatellites
    6.Compositefunctors
    7.Severalvariables
    Exercises

    Chapter4.Homology
    1.Moduleswithdifferentiation
    2.Theringofdualnumbers
    3.Gradedmodules,complexes
    4.Doublegradingsandcomplexes
    5.Functorsofcomplexes
    6.Thehomomorphism
    7.Thehomomorphism（continuation）
    8.Kiinnethrelations
    Exercises

    Chapter5.DerivedFunctors
    1.Complexesovermodules;resolutions
    2.Resolutionsofsequences
    3.Definitionofderivedfunctors
    4.Connectinghomomorphisms
    5.ThefunctorsROTandLoT
    6.Comparisonwithsatellites
    7.Computationaldevices
    8.Partialderivedfunctors
    9.Sums,products,limits
    10.Thesequenceofamap
    Exercises

    Chapter6.DerivedFunctorsofandHom
    1.ThefunctorsTorandExt
    2.Dimensionofmodulesandrings
    3.Kiinnethrelations
    4.Changeofrings
    5.Dualityhomomorphisms
    Exercises

    Chapter7.IntegralDomains
    1.Generalities
    2.Thefieldofquotients
    3.Inversibleideals
    4.Priiferrings
    5.Dedekindrings
    6.Abeliangroups
    7.AdescriptionofTort（A,C）
    Exercises

    Chapter8.AugmentedRings
    1.Homologyandcohomologyo'fanaugmentedring
    2.Examples
    3.Changeofrings
    ……
    Chapter9.AssociativeAlgebras
    Chapter10.SupplementedAlgebras
    Chapter11.Products
    Chapter12.FiniteGroups
    Chapter13.LieAlgebras
    Chapter14.Extensions
    Chapter15.SpectralSequences
    Chapter16.ApplicationsofSpectralSequences
    Chapter17.Hyperhomology
    Appendix:Exactcategories,byDavidA.Buchsbaum
    ListofSymbols
    IndexofTerminology
  • 内容简介:
    Duringthelastdecadethemethodsofalgebraictopologyhaveinvadedextensivelythedomainofpurealgebra,andinitiatedanumberofinternalrevolutions.Thepurposeofthisbookistopresentaunifiedaccountofthesedevelopmentsandtolaythefoundationsofafull-fledgedtheory.
    Theinvasionofalgebrahasoccurredonthreefrontsthroughtheconstructionofcohomologytheoriesforgroups,Liealgebras,andassociativealgebras.Thethreesubjectshavebeengivenindependentbutparalleldevelopments.Wepresenthereinasinglecohomology（andalsoahomology）theorywhichembodiesallthree；eachisobtainedfromitbyasuitablespecialization.
  • 目录:
    Preface
    Chapter1.RingsandModules
    1.Preliminaries
    2.Projectivemodules
    3.Injectivemodules
    4.Semi-simplerings
    5.Hereditaryrings
    6.Semi-hereditaryrings
    7.Noetherianrings
    Exercises

    Chapter2.AdditiveFunctors
    I.Definitions
    2.Examples
    3.Operators
    4.Preservationofexactness
    5.Compositefunctors
    6.Changeofrings
    Exercises

    Chapter3.Satellites
    1.Definitionofsatellites
    2.Connectinghomomorphisms
    3.Halfexactfunctors
    4.Connectedsequenceoffunctors
    5.Axiomaticdescriptionofsatellites
    6.Compositefunctors
    7.Severalvariables
    Exercises

    Chapter4.Homology
    1.Moduleswithdifferentiation
    2.Theringofdualnumbers
    3.Gradedmodules,complexes
    4.Doublegradingsandcomplexes
    5.Functorsofcomplexes
    6.Thehomomorphism
    7.Thehomomorphism（continuation）
    8.Kiinnethrelations
    Exercises

    Chapter5.DerivedFunctors
    1.Complexesovermodules;resolutions
    2.Resolutionsofsequences
    3.Definitionofderivedfunctors
    4.Connectinghomomorphisms
    5.ThefunctorsROTandLoT
    6.Comparisonwithsatellites
    7.Computationaldevices
    8.Partialderivedfunctors
    9.Sums,products,limits
    10.Thesequenceofamap
    Exercises

    Chapter6.DerivedFunctorsofandHom
    1.ThefunctorsTorandExt
    2.Dimensionofmodulesandrings
    3.Kiinnethrelations
    4.Changeofrings
    5.Dualityhomomorphisms
    Exercises

    Chapter7.IntegralDomains
    1.Generalities
    2.Thefieldofquotients
    3.Inversibleideals
    4.Priiferrings
    5.Dedekindrings
    6.Abeliangroups
    7.AdescriptionofTort（A,C）
    Exercises

    Chapter8.AugmentedRings
    1.Homologyandcohomologyo'fanaugmentedring
    2.Examples
    3.Changeofrings
    ……
    Chapter9.AssociativeAlgebras
    Chapter10.SupplementedAlgebras
    Chapter11.Products
    Chapter12.FiniteGroups
    Chapter13.LieAlgebras
    Chapter14.Extensions
    Chapter15.SpectralSequences
    Chapter16.ApplicationsofSpectralSequences
    Chapter17.Hyperhomology
    Appendix:Exactcategories,byDavidA.Buchsbaum
    ListofSymbols
    IndexofTerminology
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