同調代數 [Homological Algebra] epub pdf mobi txt 電子書 下載 2024

同調代數 [Homological Algebra] epub pdf mobi txt 電子書 下載 2024

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同調代數 [Homological Algebra] epub pdf mobi txt 電子書 下載 2024

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內容簡介

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.

內頁插圖

目錄

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

同調代數 [Homological Algebra] epub pdf mobi txt 電子書 下載 2024

同調代數 [Homological Algebra] 下載 epub mobi pdf txt 電子書

評分☆☆☆☆☆

經典書籍。

評分☆☆☆☆☆

吟誦愛與希望的安德烈?德昂

評分☆☆☆☆☆

袋鼠拓撲方麵的經典之一，還有一本《Foundation of Algebraic Topology》也是經典。要是也能影印齣版就好瞭。

評分☆☆☆☆☆

原版好書!值得珍惜！

評分☆☆☆☆☆

好

評分☆☆☆☆☆

歡迎您撰寫這本書的原創書評

評分☆☆☆☆☆

安德魯· 德翰（André Dahan）於1935年齣生於阿爾及利亞，日後到巴黎留學，從國立巴黎藝大學畢業後，在巴黎裝飾美術學校教書，目前與妻子與女兒居住於巴黎。德翰很晚纔開始他的繪本創作生涯，於五十二歲纔推齣第一部繪本作品《月亮你好嗎？》，他已發錶的二十多冊作品在全世界廣受歡迎，已於十幾國推齣譯本。

評分☆☆☆☆☆

賺我的錢，泡我的妞。。。

評分☆☆☆☆☆

袋鼠拓撲方麵的經典之一，還有一本《Foundation of Algebraic Topology》也是經典。要是也能影印齣版就好瞭。

类似图書 點擊查看全場最低價