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This book is on abstract algebra, 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 understand the information presented in thee Algebra, and Linear Algebra books.

[ Contents

1. Abstract algebraic systems
2. Introduction
   1. Sets
   2. Equivalence relations and congruence classes
   3. Functions
   4. Binary Operations
   5. Linear Algebra
   6. Number Theory
3. Group theory
   1. Groups
4. Rings
   1. Rings
   2. Ring Homomorphisms
   3. Ideals
   4. Integral domains
   5. Fraction Fields
   6. Polynomial Rings
5. Fields
   1. Fields
   2. Factorization
   3. Splitting Fields and Algebraic Closues
   4. Separability, Normal Extensions
6. Vector Spaces
   1. Vector Spaces
7. Modules
   1. Modules
   2. Hypercomplex numbers
8. Algebras
   1. Algebras
   2. Boolean algebra
   3. Clifford Algebras
   4. Quaternions
   5. Galois Theory
9. Further abstract algebra
   1. Category theory
   2. Lattice theory
   3. Matroids
10. Authors

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• See Subject:Algebra