同調代數 [Homological Algebra] 下載 mobi epub pdf 電子書 2025

簡體網頁||繁體網頁

☆☆☆☆☆

嘉當（Henri Cartan） 等 著

齣版社： 世界圖書齣版公司

ISBN：9787510037474

版次：1

商品編碼：10914295

包裝：平裝

外文名稱：Homological Algebra

開本：24開

齣版時間：2011-07-01

頁數：390

正文語種：英文

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

評分☆☆☆☆☆

嘉當的書，非常好，代數參考書目，值得買

評分☆☆☆☆☆

吟誦愛與希望的安德烈?德昂

評分☆☆☆☆☆

手頭常備書，學代數同調書要有的

評分☆☆☆☆☆

同調代數教材，大師之作，經典。

評分☆☆☆☆☆

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

評分☆☆☆☆☆

好書，可解模型，值得擁有

評分☆☆☆☆☆

挺不錯的，大師的手筆就是不同凡響，原以為會是法語版的，還好拿到貨的時候看是英文版的，很不錯的！

評分☆☆☆☆☆

好

評分☆☆☆☆☆

貨好，速度快，快遞服務質量好。