First Course in Abstract Algebra

ISBN-10: 0201763907
ISBN-13: 9780201763904
Edition: 7th 2003 (Revised)
Authors: John B. Fraleigh
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Description: This is an in-depth introductory text for those on an abstract algebra course. It focuses on groups, rings, and fields, giving a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

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Book details

List price: $193.80
Edition: 7th
Copyright year: 2003
Publisher: Addison Wesley
Publication date: 11/6/2002
Binding: Hardcover
Pages: 590
Size: 8.00" wide x 9.50" long x 1.00" tall
Weight: 2.398
Language: English

This is an in-depth introductory text for those on an abstract algebra course. It focuses on groups, rings, and fields, giving a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

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

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