Definition:Algebraic Structure

From ProofWiki
Jump to navigation Jump to search


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.