Definition:Algebraic Structure

Definition
An algebraic structure is a set $S$ which has one or more binary operations $\circ_1, \circ_2, \ldots, \circ_n$ defined on all the elements of $S \times S$, and is denoted $\left({S, \circ_1, \circ_2, \ldots, \circ_n}\right)$.

$\left({S, \circ}\right)$ or $\left({T, *}\right)$, etc. are symbols often used for the general algebraic structure with one (binary) operation.

Also see

 * Algebraic System, a slightly more general concept.

If $\left({S, \circ}\right)$ is an algebraic structure then $S$ is referred to as the underlying set of $\left({S, \circ}\right)$.