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ÊéÃûABSTRACT
ALGEBRA
An Introduction
×÷ÕßTHOMAS W. HUNGERFORD
Saint Louis University
Ò³Êý621
³ö°æÉçBROOKS/COL
ISBN-13: 978-1-111-56962-4
Preface ix
To the Instructor xii
To the Student xiv
Thematic Table of Contents for the Core Course xvi
Part 1 The Core Course
CHAPTER 1 Arithmetic inZRevisited 3
1.1 The Division Algorithm 3
1.2 Divisibility 9
1.3 Primes and Unique Factorization 17
CHAPTER 2 Conuruence inZandModularArithmetic 25
2.1 Congruence and Congruence Classes 25
2.2 Modular Arithmetic 32
2.3 The Structure of Z,, (p Prime) and Zn 37
CHAPTER 3 Rings 43
3.1 Definition and Examples of Rings 44
3.2 Basic Properties of Rings 59
3.3 Isomorphisms and Homomorphisms 70
CHAPTER 4 Arithmetic in f[x] 85
4.1 Polynomial Arithmetic and the Division Algorithm 86
4.2 Divisibility in f[x] 95
4.3 lrreducibles and Unique Factorization 100
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