Simple Algebraic Structures

If you've taken some "modern algebra" in college or have read up on algebraic structures, then you've probably heard of things like groups, rings, and fields. But how about semigroups, groupoids, quasigroups, loops, and monoids? Read on and you will learn all about them. This document gives the definitions for well-known algebraic structures simpler than a group. No theorems are given since this is meant to be just a dictionary of definitions.

The document is divided into the following sections:

Higher quality versions of this document are available from the groupoids index page.

Go to electronic publications page
Go to MathPro Press home page

Copyright © 1995 by MathPro Press, Inc.
Individuals may download, print, and make copies of this document for their own personal use. Commercial use prohibited.

Suggestions about format and content are welcome. Are we missing any well-known structures?

Another source of information that you might find useful is

This page is maintained by MathPro Press (
This page last modified January 31, 1995.