commutator

noun

1. 1

   An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.

2. 2

   A binary map in a given group G, given by [g, h] = ghg−1h−1, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h.

3. 3

   A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zero element if and only if the multiplication operation commutes for a and b.