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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:

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  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. Composition series
    10. The Sylow Theorems
  3. Rings
    1. Rings
    2. Ring Homomorphisms
    3. Ideals
    4. Integral domains
    5. Fraction Fields
    6. Polynomial Rings
    7. Modules
    8. Projective line
  4. Fields
    1. Fields
    2. Factorization
    3. Splitting Fields and Algebraic Closures
    4. Separability, Normal Extensions
    5. Galois Theory
  5. Vector Spaces
    1. Vector Spaces
  6. Algebras
    1. Algebras
    2. Boolean algebra
    3. Clifford Algebras
    4. Shear and Slope
    5. Quaternions
    6. 2x2 real matrices
    7. 3x3 real matrices
    8. Hypercomplex numbers
  7. Further abstract algebra
    1. Category theory
    2. Lattice theory
    3. Matroids
  8. Authors

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Pages in progress

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

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