In algebra, the commutant A of a subset S of an algebra over a field K is the subset S′ of elements of A commuting with every element of S. In other words,

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

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

See also

• Bicommutant
• von Neumann bicommutant theorem

Group theory