内容提要 本书适用于数学专业的研究生。本书已是第四版，前几版中出现的一些错误已经被更正。尤其是在前几版中出现的同调分类定理的分裂构造法已被正确的证明方法所取代，且容许短正合列的公理已经得到修正。 目录 IntroductionChapter I. Modules, Diagrams, and Functors 1. The Arrow Notation 2. Modules 3. Diagrams 4. Direct Sums 5. Free and Projective Modules 6. The Functor Horn 7. Categories 8. FunctorsChapter If. Homology of Complexes 1. Differential Groups 2. Complexes 3. Cohomology 4. The Exact Homology Sequence 5. Some Diagram Lemmas 6. Additive Relations 7. Singular Homology 8. Homotopy 9. Axioms for HomologyChapter III. Extensions and Resolutions 1. Extensions of Modules 2. Addition of Extensions 3. Obstructions to the Extension of Homomorphisms 4. The Universal Coefficient Theorem for Cohomology 5. Composition of Extensions 6. Resolutions 7. Injective Modules 8. Injective Resolutions 9.Two Exact Sequences for Extn 10. Axiomatic Description of Ext 11. The Injective EnvelopeChapter IV. Cohomol0gy of Groups 1. The Group Ring 2. Crossed Homomorphisms 3. Group Extensions 4. Factor Sets 5. The Bar Resolution 6. The Characteristic Class of a Group Extension 7. Cohomology of Cyclic and Free Groups 8. Obstructions to Extensions 9. Realization of Obstructions 10. SCHUR'S Theorem 11. Spaces with OperatorsChapter V. Tensor and Torsion Products 1. Tensor Products 2. Modules over Commutative Rings 3. Bimodules 4. Dual Modules 5. Right Exactness of Tensor Products . 6. Torsion Products of Groups 7. Torsion Products of Modules 8. Torsion Producty Resolutions 9. The Tensor Product of Complexes 10. The KONNETH Formula 11. Universal Coefficient TheoremsChapter VI. Types of Algebras 1. Algebray Diagrams 2. Graded Modules 3. Graded Algebras 4. Tensor Products of Algebras 5. Modules over Algebras 6. Cohomology of free Abelian Groups 7. Differential Graded Algebras 8. Identities on Horn and 9.Coalgebras and HoPF AlgebrasChapter VII. Dimension 1. Homological Dimension 2. Dimensions in Polynomial Rings 3. Ext and Tor for Algebras 4. Global Dimensions of Polynomial Rings 5. Separable Algebras 6. Graded Syzygies 7. Local RingsChapter VIII. Products 1. Homology Products 2. The Torsion Product of Algebras 3. A Diagram Lemma 4. External Products for Ext 5. Simplicial Objects 6. Normalization 7. Acyclic Models 8. The EILENBERG-ZILBER Theorem 9. Cup ProductsChapter IX. Relative Homological Algebra 1. Additive Categories 2. Abelian Categories 3. Categories of Diagrams 4. Comparison of Allowable Resolutions 5. Relative Abelian Categories 6, Relative Resolutions 7. The Categorical Bar Resolution 8. Relative Torsion Products 9. Direct Products of RingsChapter X. Cohomology of Algebraic SystemsChapter XI. Spectral SequencesChapter XII. Derived FunctorsBibliographyList of Standard SymbolsIndex 作者介绍 SaundersMacLanewasbornonAugust4，1909inConnecticut.HestudiedatYaleUniversityandthenattheUniversityofChicagoandatG6ttingen，wherehereceivedtheD.Phil.in1934.HehastaughtatHarvard，Cornel1andtheUniversityofChicago.MacLanesinitialresearchwasinlogicandinalgebraicnumbertheory（valuationtheory）.WithSamuelEilenberghepublishedfifteenpapersonalgebraictopology.Anumberoftheminvolvedtheinitialstepsinthecohomologyofgroupsandinotheraspectsofhomologicalalgebra-aswellasthediscoveryofcategorytheory.HisfamousundergraduatetextbookSurveyofmodernalgebra，writtenjointlywithG.Birkhoff，hasremainedinprintforover50years.MacLaneisalsotheauthorofseveralotherhighlysuccessfulbooks. 序言
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