同调代数导论-第2版-(影印版)

Preface to the Second EditionHow to Read This Book Chapter 1 Introduction1．1 SimpliciaIHomology1．2 Categories and Functors1．3 Singular HomologyChapter 2 Hom and Tensor2．1 Modules2．2 Tensor Products2．2．1 AdjointlsomorphismsChapter 3 Special Modules3．1 Projective Modules3．2 InjectiveModules3．3 Flat Modules3．3．1 PurityChapter 4 Specific Rings4．1 Semisimple Rings4．2 von Neumann Regular Rings4．3 Hereditary and Dedekind Rings4．4 Semihereditary and Prufer Rings4．5 Quasi-Frobenius Rings4．6 Semiperfect Rings4．7 Localization4．8 Polynomial RingsChapter 5 Setting the Stage5．1 Categorical Constructions5．2 Limits5．3 Adjoint Functor Theorem for Modules5．4 Sheaves5．4．1 Manifolds5．4．2 Sheaf Constructions5．5 Abelian Categories5．5．1 ComplexesChapter 6 Homology6．1 Homology Functors6．2 Derived Functors6．2．1 Left Derived Functors6．2．2 Axioms6．2．3 Covariant Right Derived Functors6．2．4 Contravariant Right Derived Functors6．3 Sheaf Cohomology6．3．1 Cech Cohomology6．3．2 Riemann-Roch TheoremChapter 7 Tor and Ext7．1 Tor7．1．1 Domains7．1．2 Localization7．2 Ext7．2．1 Baer Sum7．3 Cotorsion Groups7．4 Universal CoefficientsChapter 8 Homology and Rings8．1 Dimensions ofRings8．2 Hilbert's Syzygy Theorem8．3 Stably Free Modules8．4 Commutative Noetherian Local RingsChapter 9 Homology and Groups9．1 Group Extensions9．1．1 Semidirect Products9．1．2 General Extensions and Cohomology9．1．3 Stabilizing Automorphisms9．2 Group Cohomology9．3 Bar Resolutions9．4 Group Homology9．4．1 Schur Multiplier9．5 Change of Groups9．5．1 Restriction and Inflation9．6 Transfer9．7 Tate Groups9．8 Outer Automorphisms of p-Groups9．9 Cohomological Dimension9．10 Division Rings and Brauer GroupsChapter 10 Spectral Sequences10．1 Bicomplexes10．2 Filtrations and Exact Couples10．3 Convergence10．4 Homology of the Total Complex10．5 Cartan-Eilenberg Resolutions10．6 Grothendieck Spectral Sequences10．7 Groups10．8 Rings10．9 Sheaves10．10 Kunneth TheoremsReferencesSpecial NotationIndex