同调代数是由世界图书出版公司在2来自011年出版的图书，作者是法国的嘉款互备当。

• 书名 同调代数
• 出版社 世界图书出版公司
• 出版时间 2011年7月
• 定价 59 元
• 开本 24 开

目录

　　preface

　　c来自hapter i. rings and modules

　　1. prelimina答何年ries

　　2. pro360百科jective modules

　　3. inje雷庆酒仅叶ctive modules

　　4. semi-simple rings

　　5. here倒职鲁逐宽消先列ditary rings

　　6. semi-hereditary rings

　　7. noetherian tings

　　exercises

　　chapter ii. additive functors

　　1. definiti龙末显草掉适卫命圆义样ons

　　2. examples

　　3. operators

　　4. preservation of exactness

　　5. composite functors

　　6. change of rings

　　exercises

　　chapter iii. satellites

　据护木　1. definition of satellites

　　2. connecting homomorphisms

　　3. half exact functors

　　4. connected s染鸡面苦汽句与equence of functors

　　5. axiomatic description of satellites

　　6. composite functors

　　7. several variables

　　exercises

　　chapter iv. homology

　　1. modules with differentiation

　　2. the ring of dual n系剂裂umbers

　　3安应绝副势向危. graded modules, complexes

　　4. double 责效纪取球样止史时回gradings and complexes

　　5. func威胶利食田冲迅tors of complexes

　　6. the homomorphism

　　7. the homomorphism a (continuat陆肉又父ion)

　　8. kiinneth relations

　　exercises

　　chapter v. derived func父历视切tors

　　1. complexes over module轻必余s; resolutions

球直轻祖战示胜请　　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磁. partial derived functors

　　9. sums, products, limits

　　i0. the sequence of a map

　　exercises

　　chapter 案落似被石安呼vi. derived functors 少景of ~ and hem

　　1. the functors tor and ext

　　2. dimension of modules and rings

　　3. kiinneth relations

　　4. change of rings

　　5. duality homomorphisms

　　自永胞止细exercises

　　chapter vli. 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 torx (a,c)

　　exercises

　　chapter viii. augmented rings

　　1. homology and cohomology of an augmented ring

　　2. examples

　　3. change of rings

　　4. dimension

　　5. faithful systems

　　6. applications to graded and local rings

　　exercises

　　chapter ix. associative algebras

　　1. algebras and their tensor products

　　2. associativity formulae

　　3. the enveloping algebra a~

　　4. homology and cohomology of algebras

　　5. the hochschild groups as functors of a

　　6. standard complexes

　　7. dimension

　　exercises

　　chapter x. supplemented algebras

　　1. homology of supplemented algebras

　　2. comparison with hochschild groups

　　3. augmented monoids

　　4. groups

　　5. examples of resolutions

　　6. the inverse process

　　7. subalgebras and subgroups

　　8. weakly injective and projective modules

　　exercises

　　chapter xi. products

　　1. external products

　　2. formal properties of the products

　　3. lsomorphisms

　　4. internal products

　　5. computation of products

　　6. products in the hochschild theory

　　7. products for supplemented algebras

　　8. associativity formulae

　　9. reduction theorems

　　exercises

　　chapter xii. finite groups

　　1. norms

　　2. the complete derived sequence

　　3. complete resolutions

　　4. products for finite groups

　　5. the uniqueness theorem

　　6. duality

　　7. examples

　　8. relations with subgroups

　　9. double cosets

　　10. p-groups and sylow groups

　　1. periodicity

　　exercises

　　chapter xlli. lie algebras

　　1. lie algebras and their enveloping algebras

　　2. homology and cohomology of lie algebras

　　3. the poincare-witt theorem

　　4. subaigebras and ideals

　　5. the diagonal map and its applications

　　6. a relation in the standard complex

　　7. the complex v(g)

　　8. applications of the complex v(g)

　　exercises

　　chapter xiv. extensions

　　1. extensions of modules

　　2. extensions of associative algebras

　　3. extensions of supplemented algebras

　　4. extensions of groups

　　5. extensions of lie algebras

　　exercises

　　chapter xv. spectral sequences

　　1. filtrations and spectral sequences

　　2. convergence

　　3. maps and homotopies

　　4. the graded case

　　5. induced homomorphisms and exact sequences

　　6. application to double complexes

　　7. a generalization

　　exercises

　　chapter xvi. applications of spectral sequences

　　1. partial derived functors

　　2. functors of complexes

　　3. composite functors

　　4. associativity formulae

　　5. applications to the change of rings

　　6. normal subalgebras

　　7. associativity formulae using diagonal maps

　　8. complexes over algebras

　　9. topological applications

　　10. the almost zero theory

　　exercises

　　chapter xvll. hyperhomology

　　1. resolutions of complexes

　　2. the invariants

　　3. regularity conditions

　　4. mapping theorems

　　5. kiinneth relations

　　6. balanced functors

　　7. composite functors

　　appendix: exact categories, by david a. buchsbaum

　　list of symbols

　　index of terminology

内容简介

　　本书是数学发展史上的一个里程碑，在很长一段时间，这是本讲述拓扑代数的教程。这本书堪称是一部同调代数经典，1956年初版，至今已有七次重印出版。这本书曾在纯代数领域引起过不小的轰动，作者企图将这个领域统一起来，并且为这个领域构建一个完整的框架。书中讲述的同调理论包含了群、李代数和结合代数上同调结构，大量的结果都包括在一般框架之中，但每个结果都有不同的讲述方式，并且每个理论的特殊性质都给出了具体的讲述。本书以环上的模作为出发点，基本计算有二模张量积，以及一个模到其他模的全部同态群。函子和导出函子也是自然而然的进行了讲述。目次:环和模;加性函数;卫星;同调;导出函子;u和hom的导出函子;积分域;增广环;结合代数;补充代数;乘积;有限群;李代数;扩张;谱序列;谱序列应用;超拓扑 。