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同调

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作者：(美国)莱恩(Saunders Mac Lane) 著

出版社：上海世界图书出版公司

出版时间：2009-08

I S B N：9787510005015

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同调

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同调

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同调

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同调(英文影印版)

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《同调（英文版）》是由世界图书出版公司出版的。

内容简介

《同调(英文版)》讲述了：In presenting this treatment of homological algebra, it is a pleasureto acknowledge the help and encouragement which I have had fromall sides. Homological algebra arose from many sources in algebra andtopology. Decisive examples came from the study of group extensionsand their factor sets, a subject I learned in joint work with OTTO SCHIL-LING. A further development of homological ideas, with a view to theirtopological applications, came in my long collaboration with SAHUELEZLENBERG

作者简介

Introduction
Chapter 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. Functors

Chapter Ⅱ. 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 Homology

Chapter 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 Envelope

Chapter Ⅳ. Cohomol0gy of Groups
1. The Group Ring
2. Crossed Homomorphisms
3. Group Extensions<