Book:Allan Clark/Elements of Abstract Algebra

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

Source work progress
* : Chapter $3$: Field Theory: Definition and Examples of Field Structure: $\S 87$