Definition:Algebraic Structure

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

An algebraic structure with one (binary) operation is thus an ordered pair which can be denoted $\left({S, \circ}\right)$ or $\left({T, *}\right)$, etc.

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

 * Definition:Closed Algebraic Structure
 * Definition:Magma
 * Definition:Algebraic System, a slightly more general concept.


 * Definition:Underlying Set of Structure: the set $S$ is referred to as the underlying set of $\left({S, \circ}\right)$.