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

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• See Subject:Algebra