同调代数教程（英文版）

图书标准信息

• 作者 P.J.Hilton、U.Stammbach 编
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 2
• ISBN 9787506260077
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 364页
• 正文语种 英语

【内容简介】

Wehaveinserted,inthisedition,anextrachapter（ChapterX）entitled"SomeApplicationsandRecentDevelopments."Thefirstsectionofthischapterdescribeshowhomologicalalgebraarosebyabstractionfromalgebraictopologyandhowithascontributedtotheknowledgeoftopology.Theotherfoursectionsdescribeapplicationsofthemethodsandresultsofhomologicalalgebratootherpartsofalgebra.Mostofthematerialpresentedinthesefoursectionswasnotavailablewhenthistextwasfirstpublished.Naturally,thetreatmentsinthesefivesectionsaresomewhatcursory,theintentionbeingtogivetheflavorofthehomologicalmethodsratherthanthedetailsoftheargumentsandresults.

【目录】

PrefacetotheSecondEdition
Introduction
Ⅰ.Modules
1.Modules
2.TheGroupofHomomorphisms
3.SumsandProducts
4.FreeandProjectiveModules
5.ProjectiveModulesoveraPrincipalIdealDomain
6.Dualization,InjectiveModules
7.InjectiveModulesoveraPrincipalIdealDomain
8.CofreeModules
9.EssentialExtensions

Ⅱ.CategoriesandFunctors
1.Categories
2.Functors
3.Duality
4.NaturalTransformations
5.ProductsandCoproducts;UniversalConstructions
6.UniversalConstructionsContinued;Pull-backsandPush-outs
7.AdjointFunctors
8.AdjointFunctorsandUniversalConstructions
9.AbelianCategories
10.Projective,Injective,andFreeObjects

Ⅲ.ExtensionsofModules
1.Extensions
2.TheFunctorExt
3.ExtUsingInjectives
4.ComputationofsomeExt-Groups
5.TwoExactSequences
6.ATheoremofStein-SerreforAbelianGroups
7.TheTensorProduct
8.TheFunctorTor

Ⅳ.DerivedFunctors
I.Complexes
2.TheLongExactCoHomologySequence
3.Homotopy
4.Resolutions
5.DerivedFunctors
6.TheTwoLongExactSequencesofDerivedFunctors
7.TheFunctorsExtUsingProjectives
8.TheFunctorsExtUsingInjectives
9.Extandn-Extensions
10.AnotherCharacterizationofDerivedFunctors
11.TheFunctorTor
12.ChangeofRings

Ⅴ.TheKiinnethFormula
1.DoubleComplexes
2.TheKunnethTheorem
3.TheDualKunnethTheorem
4.ApplicationsoftheKunnethFormulas

Ⅵ.CohomologyofGroups
1.TheGroupRing
2.DefinitionofCoHomology
3.H,H
4.H,HwithTrivialCoefficientModules
5.TheAugmentationIdeal,Derivations,andtheSemi-DirectProduct
6.AShortExactSequence
7.TheCoHomologyofFiniteCyclicGroups
8.The5-TermExactSequences
9.H2,HopfsFormula,andtheLowerCentralSeries
10.HzandExtensions
11.RelativeProjectivesandRelativeInjectives
12.ReductionTheorems
13.Resolutions
14.The（Co）HomologyofaCoproduct
……
Ⅶ.CohomologyofLieAlgebras
Ⅷ.ExactCouplesandSpectralSequences
Ⅸ.SatellitesandHomology
Ⅹ.SomeApplicationsandRecentDevelopments
Bibliography
Index