commutator

== English == === Etymology === Back-formation from commutation (in the late 19th century), as is commutate (verb) too. === Noun === commutator (plural commutators) An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current. Synonyms: (dated) rheotrope, (dated) electrepeter (group theory) 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. (ring theory) 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. ==== Derived terms ==== ==== Translations ==== === See also === nilpotent group solvable group === Further reading === Commutative property on Wikipedia.Wikipedia == Latin == === Verb === commūtātor second/third-person singular future passive imperative of commūtō === References === “commutator”, in Gaffiot, Félix (1934), Dictionnaire illustré latin-français, Hachette. commutator in Ramminger, Johann (16 July 2016 (last accessed)), Neulateinische Wortliste: Ein Wörterbuch des Lateinischen von Petrarca bis 1700‎[1], pre-publication website, 2005-2016