同调

图书标准信息

• 作者 [美]莱恩 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005015
• 定价 50.00元
• 装帧 平装
• 开本 大32开
• 纸张 胶版纸
• 页数 422页
• 正文语种 英语

【内容简介】

　　Inpresentingthistreatmentofhomologicalalgebra，itisapleasuretoacknowledgethehelpandencouragementwhichIhavehadfromallsides.Homologicalalgebraarosefrommanysourcesinalgebraandtopology.Decisiveexamplescamefromthestudyofgroupextensionsandtheirfactorsets，asubjectIlearnedinjointworkwithOTTOSCHIL-LING.Afurtherdevelopmentofhomologicalideas，withaviewtotheirtopologicalapplications，cameinmylongcollaborationwithSAHUELEZLENBERG;tobothcollaborators，especialthanks.FormanyyearstheAirForceOfficeofScientificResearchsupportedmyresearchprojectsonvarioussubjectsnowsummarizedhere;itisapleasuretoacknowledgetheirlivelyunderstandingOfbasicscience.

【作者简介】

　　SaundersMacLanewasbornonAugust4，1909inConnecticut.HestudiedatYaleUniversityandthenattheUniversityofChicagoandatG6ttingen，wherehereceivedtheD.Phil.in1934.HehastaughtatHarvard，Cornel1andtheUniversityofChicago.MacLanesinitialresearchwasinlogicandinalgebraicnumbertheory（valuationtheory）.WithSamuelEilenberghepublishedfifteenpapersonalgebraictopology.Anumberoftheminvolvedtheinitialstepsinthecohomologyofgroupsandinotheraspectsofhomologicalalgebra-aswellasthediscoveryofcategorytheory.HisfamousundergraduatetextbookSurveyofmodernalgebra，writtenjointlywithG.Birkhoff，hasremainedinprintforover50years.MacLaneisalsotheauthorofseveralotherhighlysuccessfulbooks.

【目录】

Introduction
ChapterI.Modules,Diagrams,andFunctors
1.TheArrowNotation
2.Modules
3.Diagrams
4.DirectSums
5.FreeandProjectiveModules
6.TheFunctorHorn
7.Categories
8.Functors
ChapterIf.HomologyofComplexes
1.DifferentialGroups
2.Complexes
3.Cohomology
4.TheExactHomologySequence
5.SomeDiagramLemmas
6.AdditiveRelations
7.SingularHomology
8.Homotopy
9.AxiomsforHomology
ChapterIII.ExtensionsandResolutions
1.ExtensionsofModules
2.AdditionofExtensions
3.ObstructionstotheExtensionofHomomorphisms
4.TheUniversalCoefficientTheoremforCohomology
5.CompositionofExtensions
6.Resolutions
7.InjectiveModules
8.InjectiveResolutions
9.TwoExactSequencesforExtn
10.AxiomaticDescriptionofExt
11.TheInjectiveEnvelope
ChapterIV.Cohomol0gyofGroups
1.TheGroupRing
2.CrossedHomomorphisms
3.GroupExtensions
4.FactorSets
5.TheBarResolution
6.TheCharacteristicClassofaGroupExtension
7.CohomologyofCyclicandFreeGroups
8.ObstructionstoExtensions
9.RealizationofObstructions
10.SCHURSTheorem
11.SpaceswithOperators
ChapterV.TensorandTorsionProducts
1.TensorProducts
2.ModulesoverCommutativeRings
3.Bimodules
4.DualModules
5.RightExactnessofTensorProducts.
6.TorsionProductsofGroups
7.TorsionProductsofModules
8.TorsionProductsbyResolutions
9.TheTensorProductofComplexes
10.TheKONNETHFormula
11.UniversalCoefficientTheorems
ChapterVI.TypesofAlgebras
1.AlgebrasbyDiagrams
2.GradedModules
3.GradedAlgebras
4.TensorProductsofAlgebras
5.ModulesoverAlgebras
6.CohomologyoffreeAbelianGroups
7.DifferentialGradedAlgebras
8.IdentitiesonHornand
9.CoalgebrasandHoPFAlgebras
ChapterVII.Dimension
1.HomologicalDimension
2.DimensionsinPolynomialRings
3.ExtandTorforAlgebras
4.GlobalDimensionsofPolynomialRings
5.SeparableAlgebras
6.GradedSyzygies
7.LocalRings
ChapterVIII.Products
1.HomologyProducts
2.TheTorsionProductofAlgebras
3.ADiagramLemma
4.ExternalProductsforExt
5.SimplicialObjects
6.Normalization
7.AcyclicModels
8.TheEILENBERG-ZILBERTheorem
9.CupProducts
ChapterIX.RelativeHomologicalAlgebra
1.AdditiveCategories
2.AbelianCategories
3.CategoriesofDiagrams
4.ComparisonofAllowableResolutions
5.RelativeAbelianCategories
6,RelativeResolutions
7.TheCategoricalBarResolution
8.RelativeTorsionProducts
9.DirectProductsofRings
ChapterX.CohomologyofAlgebraicSystems
ChapterXI.SpectralSequences
ChapterXII.DerivedFunctors
Bibliography
ListofStandardSymbols
Index