First Course in Abstract Algebra

Name: First Course in Abstract Algebra
Price: 77.1 USD
Availability: InStock
ISBN: 9780201534672

ISBN-10: 0201534673

ISBN-13: 9780201534672

Edition: 5th 1994

Authors: John B. Fraleigh, Victor J. Katz

List price: $94.00

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Description:

Taking a classical approach to abstract algebra while integrating current applications of the subject, the new edition of this bestselling algebra text remains easily accessible and interesting. The book includes a review chapter covering basic linear algebra and proofs plus historical notes written by Victor Katz, an authority in the history of mathematics.

Book details

List price: $94.00
Edition: 5th
Copyright year: 1994
Publisher: Addison-Wesley Longman, Incorporated
Binding: Hardcover
Pages: 576
Size: 6.59" wide x 9.50" long x 1.03" tall
Weight: 2.156
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