同调代数

图书标准信息

• 作者 嘉当（Henri Cartan）、嘉当（Henri Cartan） 著
• 出版社 世界图书出版公司
• 出版时间 2011-07
• 版次 1
• ISBN 9787510037474
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 390页
• 正文语种 英语

【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