# Abstract Algebra

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
- Vector Spaces
- Modules
- Algebras
- 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

- Definition of groups, very basic properties
- Definition of subgroups, very basic properties
- Cosets, normal subgroups
- Homomorphisms, the Noether isomorphism theorems
- Commutators
- The symmetric group
- Representations
- The Sylow theorems
- Normal series
- Abelian groups

### Rings

- Rings, ideals, ring homomorphisms
- The hierarchy of rings
- Polynomial rings, irreducibility
- Fields of fractions