An Introduction to Homological Algebra

Northcott

doi:10.1017/CBO9780511565915

Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for specialists. It can also be used as a textbook for an advanced course.

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An Introduction to Homological Algebra

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xii

1 - Generalities concerning modules
pp 1-15

2 - Tensor products and groups of homomorphisms
pp 16-29

3 - Categories and functors
pp 30-45

4 - Homology functors
pp 46-62

5 - Projective and injective modules
pp 63-89

6 - Derived functors
pp 90-120

7 - Torsion and extension functors
pp 121-154

8 - Some useful identities
pp 155-173

9 - Commutative Noetherian rings of finite global dimension
pp 174-210

10 - Homology and cohomology theories of groups and monoids
pp 211-265

Notes
pp 266-277

References
pp 278-280

Index
pp 281-282

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