Book:Allan Clark/Elements of Abstract Algebra

Subject Matter

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

Contents

 * Introduction


 * Set Theory
 * The notation and terminology of set theory
 * Mappings
 * Equivalence relations
 * Properties of natural numbers


 * Group Theory
 * Definition of group structure
 * Examples of group structure
 * Subgroups and cosets
 * Conjugacy, normal subgroups, and quotient groups
 * The Sylow theorems
 * Group homomorphism and isomorphism
 * Normal and composition series
 * The Symmetric groups


 * Field Theory
 * Definition and examples of field structure
 * Vector spaces, bases and dimension


 * Galois Theory
 * Automorphisms
 * Galois extensions
 * Solvability of Equations by radicals


 * Ring Theory
 * Definition and examples of ring structure
 * Ideals
 * Unique factorization


 * Classical Ideal Theory
 * Fields of fractions
 * Dedekind domains
 * Integral extensions
 * Algebraic integers