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内容简介

During the last decade the methods of algebraic topology have invaded extensively the domain of pure algebra, and initiated a number of internal revolutions. The purpose of this book is to present a unified account of these developments and to lay the foundations of a full-fledged theory.
The invasion of algebra has occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. The three subjects have been given independent but parallel developments. We present herein a single cohomology （and also a homology） theory which embodies all three； each is obtained from it by a suitable specialization.

内页插图

目录

Preface
Chapter 1. Rings and Modules
1. Preliminaries
2. Projective modules
3. Injective modules
4. Semi-simple rings
5. Hereditary rings
6. Semi-hereditary rings
7. Noetherian rings
Exercises

Chapter 2. Additive Functors
I. Definitions
2. Examples
3. Operators
4. Preservation of exactness
5. Composite functors
6. Change of rings
Exercises

Chapter 3. Satellites
1. Definition of satellites
2. Connecting homomorphisms
3. Half exact functors
4. Connected sequence of functors
5. Axiomatic description of satellites
6. Composite functors
7. Several variables
Exercises

Chapter 4. Homology
1. Modules with differentiation
2. The ring of dual numbers
3. Graded modules, complexes
4. Double gradings and complexes
5. Functors of complexes
6. The homomorphism
7. The homomorphism （continuation）
8. Kiinneth relations
Exercises

Chapter 5. Derived Functors
1. Complexes over modules; resolutions
2. Resolutions of sequences
3. Definition of derived functors
4. Connecting homomorphisms
5. The functors ROT and LoT
6. Comparison with satellites
7. Computational devices
8. Partial derived functors
9. Sums, products, limits
10. The sequence of a map
Exercises

Chapter 6. Derived Functors of and Hom
1. The functors Tor and Ext
2. Dimension of modules and rings
3. Kiinneth relations
4. Change of rings
5. Duality homomorphisms
Exercises

Chapter 7. Integral Domains
1. Generalities
2. The field of quotients
3. Inversible ideals
4. Priifer rings
5. Dedekind rings
6. Abelian groups
7. A description of Tort （A,C）
Exercises

Chapter 8. Augmented Rings
1. Homology and cohomology o'f an augmented ring
2. Examples
3. Change of rings
……
Chapter 9. Associative Algebras
Chapter 10. Supplemented Algebras
Chapter 11. Products
Chapter 12. Finite Groups
Chapter 13. Lie Algebras
Chapter 14. Extensions
Chapter 15. Spectral Sequences
Chapter 16. Applications of Spectral Sequences
Chapter 17. Hyperhomology
Appendix: Exact categories, by David A. Buchsbaum
List of Symbols
Index of Terminology

前言/序言

同调代数 [Homological Algebra] 电子书 下载 mobi epub pdf txt

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很棒

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吟诵爱与希望的安德烈?德昂

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好

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黄筱茵◎儿童文学工作者

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评分☆☆☆☆☆

　　德昂的作品主题鲜明。他最喜欢描摹令人动容的友情。在他的笔下，我们可以与最不可能企及的对象成为一辈子的好友。在《月亮，你好吗》中，男孩划船外出，在湖面上遇见澄净的月亮。男孩与月亮愉快地一同嬉闹，后来月亮兴奋过度而摔了个大跟斗，猛一翻跌进湖里。故事的高潮在男孩帮月亮登上他的小船后节节升高。他带月亮回家，和月亮一起弹琴歌唱、旋转跳舞，两个好友一块读故事、一同温馨进餐。德昂让这段醇美的友情美好的一如每个读者可能梦想的最棒梦境一般。当我们看到玩累的月亮在床上安眠，从窗畔瞥见男孩

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这本老书虽然年代久远，但还是很有用。。。

评分☆☆☆☆☆

同调代数教材，大师之作，经典。

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