commuta torとは 意味・読み方・使い方

名詞

commutator (plural commutators)

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

   Synonyms: (dated) rheotrope, (dated) electrepeter

2. (group theory) A binary map in a given group G, given by [g, h] = ghgh, 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. (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.

派生語

参考

• nilpotent group
• solvable group

Further reading

• Commutative property on Wikipedia.Wikipedia

参照

• commutator in Gaffiot, Félix (1934) Dictionnaire illustré latin-français, Hachette.
• commutator in Ramminger, Johann (2016 July 16 (last accessed)) Neulateinische Wortliste: Ein Wörterbuch des Lateinischen von Petrarca bis 1700‎, pre-publication website, 2005-2016