[{"word":"commutators","phonetics":[],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.","synonyms":[],"antonyms":[]},{"definition":"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.","synonyms":[],"antonyms":[]},{"definition":"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.","synonyms":[],"antonyms":[]}],"synonyms":[],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/commutator","https://en.wiktionary.org/wiki/commutators"]}]