Commutant

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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. In other words,

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

S′ forms a subsemigroup. This is analogous to the concept of a centralizer in group theory.

[edit] Properties

$S' = S''' = S'''''$
$S'' = S'''' = S''''''$

[edit] See also

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