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In algebra, the commutant of a subset <math>S<math> of an algebra over a field K, <math>A<math> is the subset <math>S'<math> of elements of <math>A<math> commuting with every element of <math>S<math>. In other words,
- <math>S'=\{x\in A: sx=xs\ \mbox{for}\ \mbox{every}\ s\in S\}<math>.
S' forms a subalgebra. This is analogous to the concept of a centralizer in group theory.
See also bicommutant, von Neumann bicommutant theorem.
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