| Preface to the Second Edition Introduction Ⅰ.Modules 1.Modules 2.The Group of Homomorphisms 3.Sums and Products 4.Free and Projective Modules 5.Projective Modules over a Principal Ideal Domain 6.Dualization, Injective Modules 7.Injective Modules over a Principal Ideal Domain 8.Cofree Modules 9.Essential Extensions Ⅱ.Categories and Functors 1.Categories 2.Functors 3.Duality 4.Natural Transformations 5.Products and Coproducts; Universal Constructions 6.Universal Constructions Continued ; Pull-backs and Push-outs 7.Adjoint Functors 8.Adjoint Functors and Universal Constructions 9.Abelian Categories 10.Projective, Injective, and Free Objects Ⅲ.Extensions of Modules 1.Extensions 2.The Functor Ext 3.Ext Using Injectives 4.Computation of some Ext-Groups 5.Two Exact Sequences 6.A Theorem of Stein-Serre for Abelian Groups 7.The Tensor Product 8.The Functor Tor Ⅳ.Derived Functors I.Complexes 2.The Long Exact Co Homology Sequence 3.Homotopy 4.Resolutions 5.Derived Functors 6.The Two Long Exact Sequences of Derived Functors 7.The Functors Ext Using Projectives 8.The Functors Ext Using Injectives 9.Ext and n-Extensions 10.Another Characterization of Derived Functors 11.The Functor Tor 12.Change of Rings Ⅴ.The Kiinneth Formula 1.Double Complexes 2.The Kunneth Theorem 3.The Dual Kunneth Theorem 4.Applications of the Kunneth Formulas Ⅵ.Cohomology of Groups 1.The Group Ring 2.Definition of Co Homology 3.H, H 4.H, H with Trivial Coefficient Modules 5.The Augmentation Ideal, Derivations, and the Semi-Direct Product 6.A Short Exact Sequence 7.The Co Homology of Finite Cyclic Groups 8.The 5-Term Exact Sequences 9.H2, Hopfs Formula, and the Lower Central Series 10.Hz and Extensions 11.Relative Projectives and Relative Injectives 12.Reduction Theorems 13.Resolutions 14.The（Co）Homology of a Coproduct …… Ⅶ.Cohomology of Lie Algebras Ⅷ.Exact Couples and Spectral Sequences Ⅸ.Satellites and Homology Ⅹ.Some Applications and Recent Developments Bibliography Index |
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