同调代数 [Homological Algebra] 下载 mobi epub pdf 电子书 2024

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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.

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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] 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

袋鼠拓扑方面的经典之一，还有一本《Foundation of Algebraic Topology》也是经典。要是也能影印出版就好了。

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安德鲁· 德翰（André Dahan）于1935年出生于阿尔及利亚，日后到巴黎留学，从国立巴黎艺大学毕业后，在巴黎装饰美术学校教书，目前与妻子与女儿居住于巴黎。德翰很晚才开始他的绘本创作生涯，于五十二岁才推出第一部绘本作品《月亮你好吗？》，他已发表的二十多册作品在全世界广受欢迎，已于十几国推出译本。

评分☆☆☆☆☆

好好好好好好好好好好好好好好好好好好好好好好好好好好好好好好

评分☆☆☆☆☆

嘉当的经典著作，好好读……

评分☆☆☆☆☆

吟诵爱与希望的安德烈?德昂

评分☆☆☆☆☆

经典书籍。

评分☆☆☆☆☆

看在嘉当的份上也就买了

评分☆☆☆☆☆

　　安德烈?德昂 (André Dahan)于1935年出生于阿尔及利亚，后来到巴黎留学，从国立巴黎工艺大学毕业后，在巴黎装饰美术学校教书，目前与妻子和女儿居住于巴黎。德昂虽然很晚才开始他的绘本创作生涯，于五十二岁才推出第一部绘本作品《月亮，你好吗》（My Friend the Moon），可是他作品中独树一帜、既温暖又纯真的梦幻世界，以及每一幅图画里色彩与情境的美妙共振，都强烈吸引读者的目光。德昂创造的绘本故事世界彷佛是用一块一块精巧的魔法砖头搭盖的，除却缤纷斑斓的画?面本身，故事意欲传达的信息与其间流泄的诗意都会敲开观者的心门，所以他已发表的二十多种作品在全世界广受欢迎?，已于十几国推出译本。

评分☆☆☆☆☆

名著啊，买来看看。。。

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