Book:Allan Clark/Elements of Abstract Algebra
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Allan Clark: Elements of Abstract Algebra
Published $\text {1971}$, 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
- Six: Classical Ideal Theory
- 176 - 179: Fields of fractions
- 180 - 187: Dedekind domains
- 188 - 191: Integral extensions
- 192 - 198: Algebraic integers
- Bibliography
- Index
Source work progress
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $3$: Field Theory: Vector Spaces, Bases, and Dimensions: $\S 90$