《同调代数(英文版)》是数学发展史上的一个里程碑，在很长一段时间，这是唯一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。本书由嘉当等著。

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