同调代数教程
2003-6
世界图书出版公司
P. J. Hilton,U. Stammbach
364
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We have inserted, in this edition, an extra chapter （Chapter X） entitled "Some Applications and Recent Developments." The first section of this chapter describes how homological algebra arose by abstraction from algebraic topology and how it has contributed to the knowledge of topology. The other four sections describe applications of the methods and results of homological algebra to other parts of algebra. Most of the material presented in these four sections was not available when this text was first published. Naturally, the treatments in these five sections are somewhat cursory, the intention being to give the flavor of the homological methods rather than the details of the arguments and results.
Preface to the Second EditionIntroductionⅠ.Modules1.Modules2.The Group of Homomorphisms3.Sums and Products4.Free and Projective Modules5.Projective Modules over a Principal Ideal Domain6.Dualization, Injective Modules7.Injective Modules over a Principal Ideal Domain8.Cofree Modules9.Essential ExtensionsⅡ.Categories and Functors1.Categories2.Functors3.Duality4.Natural Transformations5.Products and Coproducts; Universal Constructions6.Universal Constructions Continued ; Pull-backs and Push-outs7.Adjoint Functors8.Adjoint Functors and Universal Constructions9.Abelian Categories10.Projective, Injective, and Free ObjectsⅢ.Extensions of Modules1.Extensions2.The Functor Ext3.Ext Using Injectives4.Computation of some Ext-Groups5.Two Exact Sequences6.A Theorem of Stein-Serre for Abelian Groups7.The Tensor Product8.The Functor TorⅣ.Derived FunctorsI.Complexes2.The Long Exact Co Homology Sequence3.Homotopy4.Resolutions5.Derived Functors6.The Two Long Exact Sequences of Derived Functors7.The Functors Ext Using Projectives8.The Functors Ext Using Injectives9.Ext and n-Extensions10.Another Characterization of Derived Functors11.The Functor Tor12.Change of RingsⅤ.The Kiinneth Formula1.Double Complexes2.The Kunneth Theorem3.The Dual Kunneth Theorem4.Applications of the Kunneth FormulasⅥ.Cohomology of Groups1.The Group Ring2.Definition of Co Homology3.H, H4.H, H with Trivial Coefficient Modules5.The Augmentation Ideal, Derivations, and the Semi-Direct Product6.A Short Exact Sequence7.The Co Homology of Finite Cyclic Groups8.The 5-Term Exact Sequences9.H2, Hopfs Formula, and the Lower Central Series10.Hz and Extensions11.Relative Projectives and Relative Injectives12.Reduction Theorems13.Resolutions14.The（Co）Homology of a Coproduct……Ⅶ.Cohomology of Lie AlgebrasⅧ.Exact Couples and Spectral SequencesⅨ.Satellites and HomologyⅩ.Some Applications and Recent DevelopmentsBibliographyIndex
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