# Definition:Algebraic Structure

## Definition

An algebraic structure is an ordered tuple:

$\struct {S, \circ_1, \circ_2, \ldots, \circ_n}$

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 $\struct {S, \circ}$ or $\struct {T, *}$, and so on.

## 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 $\gen {S, \circ}$ for $\struct {S, \circ}$.

## Also see

• Results about algebraic structures can be found here.