A First Course in Abstract Algebra: With Applications

ISBN-10: 0131862677
ISBN-13: 9780131862678
Series: A First Course in Abstract Algebra
Category: Algebra, Abstract
Pages: 581
Language: English
Published: 2006
Publisher: Prentice Hall
Author: Joseph J. Rotman

Description

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.

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Other editions

A First Course in Abstract Algebra
- 2000
- 531 pages
- Paperback
- Prentice Hall
A First Course in Abstract Algebra: Rings, Groups, and Fields,...
- 2014-11-07
- 552 pages
- Ebook
- CRC Press
A First Course in Abstract Algebra: Rings, Groups and Fields,...
- 2005-01-27
- 684 pages
- Paperback
- CRC Press
A First Course in Abstract Algebra
- 2004
- 520 pages
- Paperback
- Pearson Education

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