A First Course in Abstract Algebra / Edition 1

A First Course in Abstract Algebra / Edition 1

by Joseph J. Rotman
     
 

ISBN-10: 0133113744

ISBN-13: 9780133113747

Pub. Date: 10/28/1995

Publisher: Prentice Hall Professional Technical Reference

This spectacularly clear introduction to abstract algebra is is designed to make the study of all required topics and the reading and writing of proofs both accessible and enjoyable for readers encountering the subject for the first time. Number Theory. Groups. Commutative Rings. Modules. Algebras. Principal Idea Domains. Group Theory II. Polynomials

Overview

This spectacularly clear introduction to abstract algebra is is designed to make the study of all required topics and the reading and writing of proofs both accessible and enjoyable for readers encountering the subject for the first time. Number Theory. Groups. Commutative Rings. Modules. Algebras. Principal Idea Domains. Group Theory II. Polynomials In Several Variables. For anyone interested in learning abstract algebra.

Product Details

ISBN-13:
9780133113747
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
10/28/1995
Edition description:
Older Edition
Pages:
265
Product dimensions:
6.26(w) x 9.31(h) x 0.71(d)

Related Subjects

Table of Contents

Preface to the First Editionvii
Preface to the Second Editionxi
Chapter 1Number Theory1
1.1.Induction1
1.2.Binomial Coefficients17
1.3.Greatest Common Divisors36
1.4.The Fundamental Theorem of Arithmetic58
1.5.Congruences62
1.6.Dates and Days73
Chapter 2Groups I82
2.1.Functions82
2.2.Permutations97
2.3.Groups115
Symmetry128
2.4.Lagrange's Theorem134
2.5.Homomorphisms143
2.6.Quotient Groups156
2.7.Group Actions178
2.8.Counting with Groups194
Chapter 3Commutative Rings I203
3.1.First Properties203
3.2.Fields216
3.3.Polynomials225
3.4.Homomorphisms233
3.5.Greatest Common Divisors239
Euclidean Rings252
3.6.Unique Factorization261
3.7.Irreducibility267
3.8.Quotient Rings and Finite Fields278
3.9.Officers, Fertilizer, and a Line at Infinity289
Chapter 4Goodies301
4.1.Linear Algebra301
Vector Spaces301
Linear Transformations318
Applications to Fields329
4.2.Euclidean Constructions332
4.3.Classical Formulas345
4.4.Insolvability of the General Quintic363
Formulas and Solvability by Radicals368
Translation into Group Theory371
4.5.Epilog381
Chapter 5Groups II385
5.1.Finite Abelian Groups385
5.2.The Sylow Theorems397
5.3.The Jordan-Holder Theorem408
5.4.Presentations420
Chapter 6Commutative Rings II437
6.1.Prime Ideals and Maximal Ideals437
6.2.Unique Factorization445
6.3.Noetherian Rings456
6.4.Varieties462
6.5.Grobner Bases480
Generalized Division Algorithm482
Grobner Bases493
Hints to Exercises505
Bibliography519
Index521

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