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9780471368793

Abstract Algebra

by
  • ISBN13:

    9780471368793

  • ISBN10:

    0471368792

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 1996-01-15
  • Publisher: Wiley

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Summary

Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.

Author Biography

Israel Nathan Herstein was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.

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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