Algebraic structure

In mathematics, and more specifically in abstract algebra, the term algebraic structure generally refers to a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms.

Examples of algebraic structures include groups, rings, fields, and lattices. More complex structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex algebraic structures include vector spaces, modules, and algebras.