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A First Course in Abstract Algebra
ISBN: 9780201534672 | 0201534673
Edition: 5thFormat: Hardcover
Publisher: ADDISON WESLEY LONGMAN INC
Pub. Date: 1/1/1994
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An introduction to abstract algebra. Provides valuable experience for any further axiomatic study of mathematics. DLC: Algebra, Abstract.
| Sets and Relations | |
| Groups and Subgroups | |
| Introduction and Examples | |
| Binary Operations | |
| Isomorphic Binary Structures | |
| Groups | |
| Subgroups | |
| Cyclic Groups | |
| Generators and Cayley Digraphs | |
| Permutations, Cosets, and Direct Products | |
| Groups of Permutations | |
| Orbits, C... MORE | |
| Cosets and the Theorem of Lagrange | |
| Direct Products and Finitely Generated Abelian Groups | |
| Plane Isometries | |
| Homomorphisms and Factor Groups | |
| Homomorphisms | |
| Factor Groups | |
| Factor-Group Computations and Simple Groups | |
| Group Action on a Set | |
| Applications of G-Sets to Counting | |
| Rings and Fields | |
| Rings and Fields | |
| Integral Domains | |
| Fermat's and Euler's Theorems | |
| The Field of Quotients of an Integral Domain | |
| Rings of Polynomials | |
| Factorization of Polynomials over a Field | |
| Noncommutative Examples | |
| Ordered Rings and Fields | |
| Ideals and Factor Rings | |
| Homomorphisms and Factor Rings | |
| Prime and Maximal Ideas | |
| Grouml;bner Bases for Ideals | |
| Extension Fields | |
| Introduction to Extension Fields | |
| Vector Spaces | |
| Algebraic Extensions | |
| Geometric Constructions | |
| Finite Fields | |
| Advanced Group Theory | |
| Isomorphism Theorems | |
| Series of Groups | |
| Sylow Theorems | |
| Applications of the Sylow Theory | |
| Free Abelian Groups | |
| Free Groups | |
| Group Presentations | |
| Groups in Topology | |
| Simplicial Complexes and Homology Groups | |
| Computations of Homology Groups | |
| More Homology Computations and Applications | |
| Homological Algebra | |
| Factorization | |
| Unique Factorization Domains | |
| Euclidean Domains | |
| Gaussian Integers and Multiplicative Norms | |
| Automorphisms and Galois Theory | |
| Automorphisms of Fields | |
| The Isomorphism Extension Theorem | |
| Splitting Fields | |
| Separable Extensions | |
| Totally Inseparable Extensions | |
| Galois Theory | |
| Illustrations of Galois Theory | |
| Cyclotomic Extensions | |
| Insolvability of the Quintic | |
| Appendix: Matrix Algebra | |
| Notations | |
| Answers to odd-numbered exercises not asking for definitions or proofs | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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