In 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. The notion of algebraic structure has been formalized in universal algebra.
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."
This definition of an algebraic structure should not be taken as restrictive. Anything that satisfies the axioms defining a structure is an instance of that structure, regardless of how many other axioms that instance happens to have. For example, all groups are also semigroups and magmas.
Reference:
http://en.wikipedia.org/wiki/Algebraic_structure
