内容简介

Book Description

"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

(From amazon.com)

作品目录

Part One The Basic Objects of Algebra

Chapter 1 Groups

1. Monoids

2. Groups

3. Normal subgroups

4. Cyclic groups

5. Operations of a group on a set

6. Sylow subgroups

7. Direct sums and free abelian groups

8. Finitely generated abelian groups

9. The dual group

10. Inverse limit and completion

11. Categories and functors

12. Free groups

Chapter 2 Rings

1. Rings and homomorphisms

2. Commutative rings

3. Polynomials and group rings

4. Localization

5. Principal and factorial rings

Chapter 3 Modules

Chapter 4 Polynomlals

Part Two Algebraic Equations

Chapter 5 Algebralc Extensions

Chapter 6 Galois Theory

Chapter 7 Extensions of Rings

Chapter 8 Transcendental Extensions

Chapter 9 Algebraic Spaces

Chapter 10 Noetherial Rings and Modules

Chapter 11 Real Fields

Chapter 12 Absolute Values

Part Three Liear Alebar and Reqresentations

Chapter 13 Matrices and Linear Maps

Chapter 14 Representatlon of One Endomorphism

Chapter 15 Structure of Bilinear Forms

Chapter 16 The Tensor Product

Chapter 17 Smisimplicity

Chapter 18 Representations of Finite Groups

Chapter 19 The Alternating Product

Part Four Homological Algebra

Chapter 20 General Homology Theory

Chapter 21 Finite Free Resolutions

Appendix 1 The Transcendence of e and

Appendix 2 Some Set Theory

Bibliography

Index