[[!redirects commutant]] [[!redirects center]] [[!redirects centre]] ## Definition ## Let $(A, m)$ be a [[magma]] and let $B$ be a subtype of $A$ with a [[monic function]] $i:B \subseteq A$. The __commutant__ of $B$ in $A$ is defined as $$C_A(B) \coloneqq \sum_{b:B} \prod_{a:A} m(a, i(b)) = m(i(b), a)$$ The __center__ or __centre__ of $A$ is defined as the commutant of $A$ in $A$ $$Z(A) \coloneqq C_A(A)$$ ## See also ## * [[Higher algebra]] * [[commutative A3-space]] * [[commutative monoid]] * [[abelian group]]