Algebra
Academic Press
Published on 1. November 1983
299 pages
978-0-08-087429-6 (ISBN)
Description
Algebra
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Content
- Front Cover
- Algebra
- Copyright Page
- Contents
- Preface
- List of Symbols
- Introduction
- Chapter I. Groups
- 1. Groups, Subgroups, and Homomorphisms
- 2. Permutation Groups
- 3. The Symmetric and Alternating Groups
- 4. The Sylow Theorems
- 5. Solvable Groups, Normal and Subnormal Series
- 6. Products
- 7. Nilpotent Groups
- 8. Finite Abelian Groups
- 9. Free Groups
- 10. Generators and Relations
- 11. Some Finite Groups Classified
- 12. Further Exercises
- Chapter II. Rings
- 1. Preliminaries: Ideals and Homomorphisms
- 2. The Field of Fractions of an Integral Domain
- 3. Polynomials
- 4. Polynomials in Several Indeterminates
- 5. Divisibility and Factorization
- 6. The Chinese Remainder Theorem
- 7. The Hilbert Basis Theorem
- 8. Further Exercises
- Chapter III. Fields and Galois Theory
- 1. Field Extensions
- 2. The Fundamental Theorem of Galois Theory
- 3. Normality and Separability
- 4. The Galois Theory of Equations
- 5. Symmetric Functions
- 6. Geometrical Constructions
- 7. Norm and Trace
- 8. Further Exercises
- Chapter IV. Modules
- 1. Preliminaries
- 2. Direct Sums, Free Modules
- 3. Finitely Generated Modules over a PID
- 4. Applications to Linear Algebra
- 5. Computations
- 6. Tensor Products
- 7. Further Exercises
- Chapter V. Structure of Rings and Algebras
- 1. Preliminaries
- 2. The Jacobson Radical
- 3. The Density Theorem
- 4. Artinian Rings
- 5. Further Exercises
- Chapter VI. Further Topics
- 1. Infinite Abelian Groups
- 2. PÓlya Redfield Enumeration
- 3. PSL(V)
- 4. Integral Dependence and Dedekind Domains
- 5. Transcendental Field Extensions
- 6. Valuations and p-adic Numbers
- 7. Real Fields and Sturm's Theorem
- 8. Representations and Characters of Finite Groups
- 9. Some Galois Groups
- Appendix: Zorn's Lemma
- References
- Index
- Pure and Applied Mathematics
