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:
- Introduction
- Group Theory
- Rings
- Fields
- Fields
- Factorization
- Splitting Fields and Algebraic Closures
- Separability, Normal Extensions
- Vector Spaces
- Modules
- Algebras
- Algebras
- Boolean algebra
- Clifford Algebras
- Quaternions
- 2x2 real matrices
- Galois Theory
- Further abstract algebra
- Authors
Related books
- See Subject:Algebra
Information for contributors
This wikibook shall give an introduction to the fundamental concepts of abstract algebra, such as groups, rings and ideals, and fields and Galois theory.
Contents
Groups
- Groups and subgroups
- Abelian groups
- Representations
- p-groups
Rings
- Rings, ideals, ring homomorphisms
- The hierarchy of rings
- Polynomial rings, irreducibility
- Fields of fractions
Fields
- Fields and prime fields
- Algebraic field extensions
- Elementary Galois theory
- Transcendental extensions
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