First Course in Abstract Algebra

Name: First Course in Abstract Algebra
Price: 67.95 USD
Availability: InStock
ISBN: 9780201763904

ISBN-10: 0201763907

ISBN-13: 9780201763904

Edition: 7th 2003 (Revised)

Authors: John Fraleigh

List price: $219.99

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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.

Book details

List price: $219.99
Edition: 7th
Copyright year: 2003
Publisher: Pearson Education
Publication date: 11/6/2002
Binding: Hardcover
Pages: 544
Size: 7.85" wide x 9.50" long x 1.00" tall
Weight: 2.486
Language: English



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