ENCYCLOPEDIA 4U .com

# Encyclopedia Home Page

 Web Encyclopedia4u.com

# Abstract algebra

Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers.

Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra. Because of this, abstract algebra has numerous fruitful connections to all other branches of mathematics.

Examples of algebraic structures with a single binary operation are:

• semigroups
• monoids
• groups
• quasigroups

More complicated examples include:

• rings and fields
• modules and vector spaces
• associative algebras and Lie algebras
• lattices and Boolean algebras

In universal algebra, all those definitions and facts are collected that apply to all algebraic structures alike. All the above classes of objects, together with the proper notion of homomorphism, form categories, and category theory frequently provides the formalism for translating between and comparing different algebraic structures.

External references:

Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities.

Copyright © 2005 Par Web Solutions All Rights reserved.
| Privacy

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Abstract algebra".