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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] 下載 mobi epub pdf txt 電子書

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　　德昂的作品主題鮮明。他最喜歡描摹令人動容的友情。在他的筆下，我們可以與最不可能企及的對象成為一輩子的好友。在《月亮，你好嗎》中，男孩劃船外齣，在湖麵上遇見澄淨的月亮。男孩與月亮愉快地一同嬉鬧，後來月亮興奮過度而摔瞭個大跟鬥，猛一翻跌進湖裏。故事的高潮在男孩幫月亮登上他的小船後節節升高。他帶月亮迴傢，和月亮一起彈琴歌唱、鏇轉跳舞，兩個好友一塊讀故事、一同溫馨進餐。德昂讓這段醇美的友情美好的一如每個讀者可能夢想的最棒夢境一般。當我們看到玩纍的月亮在床上安眠，從窗畔瞥見男孩安德魯· 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。

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經典書籍。

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同調代數教材，大師之作，經典。

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　　安德烈?德昂 (André Dahan)於1935年齣生於阿爾及利亞，後來到巴黎留學，從國立巴黎工藝大學畢業後，在巴黎裝飾美術學校教書，目前與妻子和女兒居住於巴黎。德昂雖然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》（My Friend the Moon），可是他作品中獨樹一幟、既溫暖又純真的夢幻世界，以及每一幅圖畫裏色彩與情境的美妙共振，都強烈吸引讀者的目光。德昂創造的繪本故事世界彷佛是用一塊一塊精巧的魔法磚頭搭蓋的，除卻繽紛斑斕的畫?麵本身，故事意欲傳達的信息與其間流泄的詩意都會敲開觀者的心門，所以他已發錶的二十多種作品在全世界廣受歡迎?，已於十幾國推齣譯本。

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