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 known as
Some sources refer to this concept as an abstract algebra, but this term is more generally used for the branch of mathematics that studies these structures.

Also denoted as
Some sources use the notation $\left \langle{S, \circ}\right \rangle$ for $\left({S, \circ}\right)$.

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 $\left({S, \circ}\right)$.