The branch of mathematics dealing with Group Theory and Coding Theory which studies number systems and operations within them. The word ``algebra'' is a distortion of the Arabic title of a treatise by al-Khwarizmi about algebraic methods. Note that mathematicians refer to the ``school algebra'' generally taught in middle and high school as ``Arithmetic,'' reserving the word ``algebra'' for the more advanced aspects of the subject.

Formally, an algebra is a Vector Space , over a Field with a Multiplication which turns it
into a Ring defined such that, if and , then

In addition to the usual algebra of Real Numbers, there are additional Consistent algebras which can be formulated by weakening the Field Axioms, at least 200 of which have been

Algebras which have been investigated and found to be of interest are usually named after one or more of their investigators. This practice leads to exotic-sounding (but unenlightening) names which algebraists frequently use with minimal or nonexistent explanation.

**References**

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1999-05-25