A Quick and Simple Dictionary

commutator

1. Noun.  an electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.
2. Noun.  (mathematics) (''of a group'') an element of the form ''ghg⁻¹h⁻¹'' where ''g'' and ''h'' are elements of the group; it is equal to the group's identity if and only if ''g'' and ''h'' commute.
3. Noun.  (mathematics) (''of a ring'') an element of the form ''ab-ba'', where ''a'' and ''b'' are elements of the ring, it is identical to the ring's zero element if and only if ''a'' and ''b'' commute.