Definition:Algebraic System

Definition
An algebraic system is a mathematical system $\mathcal S = \left({E, O}\right)$ where:


 * $E$ is a non-empty set of elements


 * $O$ is a set of finitary operations on $E$.

Also known as
Some sources refer to such an object as an algebra, but the general consensus is to reserve the term algebra for a slightly more refined concept.

Also see

 * Algebraic Structure: a refinement of this concept in which $O$ consists specifically of binary operations.