Abstract Algebra

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This book is on abstract algebra (abstract algebraic systems), an advanced set of topics related to algebra, including groups, rings, ideals, fields, and more. Readers of this book are expected to have read and understood the information presented in the Linear Algebra book, or an equivalent alternative.

Contents

This book is part of a series on Algebra:

Basic Algebra
Algebra
Intermediate Algebra
Linear Algebra
Abstract Algebra
Intro to Rings and Algebras

  1. Introduction
    1. Sets
    2. Equivalence relations and congruence classes
    3. Functions
    4. Binary Operations
    5. Linear Algebra
    6. Number Theory
  2. Group Theory
    1. Groups
    2. Subgroups
    3. Cyclic groups
    4. Permutation groups
    5. Homomorphism
    6. Normal subgroups and Quotient groups
    7. Products and Free groups
    8. Group actions on sets
    9. The Sylow Theorems
  3. Rings
    1. Rings
    2. Ring Homomorphisms
    3. Ideals
    4. Integral domains
    5. Fraction Fields
    6. Polynomial Rings
  4. Fields
    1. Fields
    2. Factorization
    3. Splitting Fields and Algebraic Closues
    4. Separability, Normal Extensions
  5. Vector Spaces
    1. Vector Spaces
  6. Modules
    1. Modules
    2. Hypercomplex numbers
  7. Algebras
    1. Algebras
    2. Boolean algebra
    3. Clifford Algebras
    4. Quaternions
    5. Galois Theory
  8. Further abstract algebra
    1. Category theory
    2. Lattice theory
    3. Matroids
  9. Authors

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