Book:Allan Clark/Elements of Abstract Algebra

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Allan Clark: Elements of Abstract Algebra

Published $1971$, Dover

ISBN 0-486-64725-0.


Subject Matter


Contents

Foreword
Introduction
One: Set Theory
1 - 9: The notation and terminology of set theory
10 - 16: Mappings
17 - 19: Equivalence relations
20 - 25: Properties of natural numbers
Two: Group Theory
26 - 29: Definition of group structure
30 - 34: Examples of group structure
35 - 44: Subgroups and cosets
45 - 52: Conjugacy, normal subgroups, and quotient groups
53 - 59: The Sylow theorems
60 - 70: Group homomorphism and isomorphism
71 - 75: Normal and composition series
76 - 86: The symmetric groups
Three: Field Theory
87 - 89: Definition and examples of field structure
90 - 95: Vector spaces, bases and dimension
96 - 97: Extension fields
98 - 107: Polynomials
108 - 114: Algebraic extensions
115 - 121: Constructions with straightedge and compass
Four: Galois Theory
122 - 126: Automorphisms
127 - 138: Galois extensions
139 - 149: Solvability of equations by radicals
Five: Ring Theory
150 - 156: Definition and examples of ring structure
157 - 168: Ideals
169 - 175: Unique factorization
Six: Classical Ideal Theory
176 - 179: Fields of fractions
180 - 187: Dedekind domains
188 - 191: Integral extensions
192 - 198: Algebraic integers
Bibliography
Index