A term used synonymously with mod ern algebra and general algebra to describe the type of algebra which has been developed since the mid-1920s and has become a basic idiom of contemporary mathematics. In contrast with the earlier algebra, which was highly computational and was con fined to the study of specific systems generally based on real and complex numbers, abstract algebra is conceptual and axiomatic and deals with systems which are arbitrary sets of elements of unspecified type, together with certain compositions satisfying prescribed lists of axioms.

A good insight into the difference between the older and the present approach can be obtained by comparing the older matrix theory with the more abstract linear algebra. Both deal with roughly the same portion of mathematics, the former a direct perspective which stresses calculations with matrices, the latter from an axiomatic and geometric viewpoint which treats vector spaces and linear transformations as the basic notions, and matrices as secondary to these. [Related topics: LINEAR ALGEBRA; MATRIX THEORY.]

Abstract algebra deals with a number of important algebraic structures, such as groups, rings, and lattices. [Related topics: GROUP THEORY; RING THEORY.]

This entry was posted on Sunday, August 20th, 2006 at 12:47 pm and is filed under Math. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.