In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition--the basic operations of algebra--are studied. Essentially no previous knowledge is required; it is only assumed as background that the reader has learned some linear algebra over the real numbers.

A publication of Vieweg Verlag. The AMS is exclusive distributor in North America. Vieweg Verlag Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.

Readership

Table of Contents

• Introduction
• Fundamentals of groups
• Fundamentals of rings and fields
• Modules
• A little more group theory
• Fields
• More field theory
• Modern linear algebra
• Quadratic and alternating forms
• Ring and field extensions
• Noetherian rings and localization
• Dedekind domains
• Representations of groups
• More modules
• Categories
• Completion
• Lie algebra
• The Clifford algebra
• Commutative rings
• Logic
• Tor's
• Glossary
• Index