algebraic structure

In universal algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties.Abstractly, an "algebraic structure," is the collection of all possible models of a given set of axioms. More concretely, an algebraic structure is any particular model of some set of axioms. For example, the monster group both "is" an algebraic structure in the concrete sense, and abstractly, "has" the group structure in common with all other groups. This article employs both meanings of "structure."
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<mathematics> Any formal mathematical system consisting of a set of objects and operations on those objects. Examples are Boolean algebra, numerical algebra, set algebra and matrix algebra.
[Is this the most common name for this concept?]
(1997-02-25)