# commutator

> English word · Noun · frequency rank #80,335

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

## Etymology
Back-formation from commutation (in the late 19th century), as is commutate (verb) too.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/commutator