9780471368793

Abstract Algebra, 3rd Edition

by
  • ISBN13:

    9780471368793

  • ISBN10:

    0471368792

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 1/1/1996
  • Publisher: Wiley

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Table of Contents

Preface ix
Things Familiar and Less Familiar
1(39)
A Few Preliminary Remarks
1(2)
Set Theory
3(5)
Mappings
8(8)
A(S) (The Set of 1--1 Mappings of S onto Itself)
16(5)
The Integers
21(8)
Mathematical Induction
29(3)
Complex Numbers
32(8)
Groups
40(68)
Definitions and Examples of Groups
40(8)
Some Simple Remarks
48(3)
Subgroups
51(5)
Lagrange's Theorem
56(10)
Homomorphisms and Normal Subgroups
66(11)
Factor Groups
77(7)
The Homomorphism Theorems
84(4)
Cauchy's Theorem
88(4)
Direct Products
92(4)
Finite Abelian Groups (Optional)
96(5)
Conjugacy and Sylow's Theorem (Optional)
101(7)
The Symmetric Group
108(17)
Preliminaries
108(3)
Cycle Decomposition
111(8)
Odd and Even Permutations
119(6)
Ring Theory
125(51)
Definitions and Examples
125(12)
Some Simple Results
137(2)
Ideals, Homomorphisms, and Quotient Rings
139(9)
Maximal Ideals
148(3)
Polynomial Rings
151(15)
Polynomials over the Rationals
166(6)
Field of Quotients of an Integral Domain
172(4)
Fields
176(39)
Examples of Fields
176(4)
A Brief Excursion into Vector Spaces
180(11)
Field Extensions
191(7)
Finite Extensions
198(3)
Constructibility
201(6)
Roots of Polynomials
207(8)
Special Topics (Optional)
215(28)
The Simplicity of An
215(6)
Finite Fields I
221(3)
Finite Fields II: Existence
224(3)
Finite Fields III: Uniqueness
227(2)
Cyclotomic Polynomials
229(7)
Liouville's Criterion
236(3)
The Irrationality of π
239(4)
Index 243

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