章节目录
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
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)
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