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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.

Table of Contents

This book is part of a series on Algebra:

A printable version of Abstract Algebra is available. (edit it)


  1. Introduction
    1. Sets
    2. Equivalence relations and congruence classes
    3. Functions
    4. Binary Operations
    5. Linear Algebra
    6. Number Theory
    7. Practice Problems
  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. Composition series
    10. The Sylow Theorems
    11. Practice Problems
  3. Rings
    1. Rings
    2. Ring Homomorphisms
    3. Ideals
    4. Integral domains
    5. Fraction Fields
    6. Polynomial Rings
    7. Modules
    8. Projective line
    9. Practice Problems
  4. Fields
    1. Fields
    2. Factorization
    3. Splitting Fields and Algebraic Closures
    4. Separability, Normal Extensions
    5. Galois Theory
    6. Practice Problems
  5. Vector Spaces
    1. Vector Spaces
    2. Practice Problems
  6. Algebras
    1. Algebras
    2. Boolean algebra
    3. Clifford Algebras
    4. Shear and Slope
    5. Quaternions
    6. 2x2 real matrices
    7. Hypercomplex numbers
    8. Practice Problems
  7. Further abstract algebra
    1. Category theory
    2. Lattice theory
    3. Matroids
    4. Practice Problems
  8. Authors

Information for contributors

Pages in progress

Abstract Algebra/The hierarchy of rings Abstract Algebra/Rings, ideals, ring homomorphisms

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