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

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

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

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] epub pdf mobi txt 电子书 下载 2024

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

评分☆☆☆☆☆

吟诵爱与希望的安德烈?德昂

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　　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☆☆☆☆☆

好书，可解模型，值得拥有

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吟诵爱与希望的安德烈?德昂

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欢迎您撰写这本书的原创书评

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这本老书虽然年代久远，但还是很有用。。。

评分☆☆☆☆☆

看在嘉当的份上也就买了

评分☆☆☆☆☆

吟诵爱与希望的安德烈?德昂

评分☆☆☆☆☆

嘉当的书，非常好，代数参考书目，值得买

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