ProofWiki:Books/Allan Clark/Elements of Abstract Algebra

Allan Clark: Elements of Abstract Algebra

Published 1971, Dover.

ISBN 0-486-64725-0

Subject Matter

• Set Theory
• Group Theory
• Field Theory
• Galois Theory
• Ring Theory
• Classical Ideal Theory

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