A First Course in Abstract Algebra

ISBN 13:
9780201534672
ISBN 10:
0201534673
Edition: 5th
Format: Hardcover
Copyright: 01/01/1994
Publisher: ADDISON WESLEY LONGMAN INC
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Note: Not guaranteed to come with supplemental materials (access cards, study guides, lab manuals, CDs, etc.)

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Summary

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, Cycles, and the Alternating Groups
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.

A First Course in Abstract Algebra

9780201534672

0201534673

Summary

Table of Contents

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