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A First Course in Abstract Algebra (3rd Edition)

A First Course in Abstract Algebra (3rd Edition)
Author: Joseph J. Rotman
ISBN 13: 9780131862678
ISBN 10: 131862677
Edition: 3
Publisher: Pearson
Publication Date: 2005-10-08
Format: Paperback
Pages: 640
List Price: $116.60

This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.

Number Theory: Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic

Congruences; Dates and Days. Groups I: Some Set Theory; Permutations; Groups; Subgroups and Lagrange's Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups. Commutative Rings I: First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons. Linear Algebra: Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms. Fields: Classical Formulas; Insolvability of the General Quintic; Epilog. Groups II: Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry. Commutative Rings III: Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases.

For all readers interested in abstract algebra.


The new edition of a textbook that introduces three related topics: number theory (division algorithm, unique factorization into primes, and congruences), group theory (permutations, Lagrange's theory, homomorphisms, and quotient groups), and commutative ring theory (domains, fields, polynomial and quotient rings, and finite fields). A final chapter combines the three topics to solve such problems as angle trisection, squaring the circle, and the construction of regular -gons. Annotation c. Book News, Inc., Portland, OR (booknews.com)