UID:
almahu_9947366444202882
Format:
1 online resource (317 p.)
ISBN:
1-281-76356-X
,
9786611763565
,
0-08-087429-0
Series Statement:
Pure and applied mathematics ; 110
Content:
Algebra
Note:
Description based upon print version of record.
,
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 Indeterminates5. 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
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6. Tensor Products7. 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
,
English
Additional Edition:
ISBN 0-12-304620-3
Language:
English
