Serge Lang

Algebra - 3rd rev. ed. - New York: Springer, [c2002] - 914 p - Graduate Texts in Mathematics Volume 211 .

Part I- The Basic Objects of Algebra
1. Groups
2. Rings
3. Modules
4. Polynomials

Part II- Algebraic Equations
5. Algebraic Extensions
6. Galois Theory
7. Extensions of Rings
8. Transcendental Extensions
9. Algebraic Spaces
10. Noetherian Rings and Modules
11. Real Fields
12. Absolute Values

Part III- Linear Algebra and Representations
13. Matrices and Linear Maps
14. Representation of One Endomorphism
15. Structure of Bilinear Forms
16. The Tensor Product
17. Semisimplicity
18. Representations of Finite Groups
19. The Alternating Product

Part IV- Homological Algebra
20. General Homology Theory
21. Finite Free Resolutions


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. This book successfully addresses all of the basic concepts of algebra. -- summary provided by publisher

9780387953854

QA154.3