同调代数教程 第2版 英文版

本书是一本比较标准的 同调代数教材，从上世纪60 年代末开始在瑞士联邦理工 学院及美国几所大学使用， 本版在第1版的基础上增加 了新内容——同调代数的应 用和新进展。本书内容比较 详细全面，基础理论十分扎 实；论述也比较深入浅出， 通俗易懂，有很好的例题和 习题。目次：范畴与函子； 模的扩张；导出函子； Kunneth公式；群的上同调 ；李代数的上同调；正合偶 和谱序列；伴随性和同调论 ；应用和最新进展。

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 Funetors 1.Complexes 2.The Long Exact (Co) Homology Sequence 3.Homotopy 4.Resolutions 5.Derived Functors 6.The Two Long Exact Sequences of Derived Functor 7.The Functors ExtnΛ Using Projectives 8.The Functors ExtnΛ Using Injectives 9.Extn and n-Extensions 10.Another Characterization bfDerived Functors 11.The Functor TotΛn 12.Change of Rings Ⅴ.The Kunneth Formula 1.Double Complexes 2.The Kiinneth Theorem 3.The Dual Kunneth Theorem 4.Applications of the Kunneth Formulas