# Commutant

In algebra, the commutant of a subset S of a semigroup (such as an algebra or a group) A is the subset S′ of elements of A commuting with every element of S.[1] In other words,

${\displaystyle S'=\{x\in A:sx=xs\ {\mbox{for}}\ {\mbox{every}}\ s\in S\}.}$

S′ forms a subsemigroup. This generalizes the concept of centralizer in group theory.