commutator

English

Noun

commutator (plural commutators)

1. An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.
2. (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.
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.

Derived terms

• anticommutator
• multicommutator

Translations

electrical switch

• Finnish: kommutaattori (fi)
• Romanian: colector de comutație n, colector (ro) n (electric)
• (deprecated template usage) {{trans-mid}}
• Swedish: kommutator (sv) c

binary function in a group

• Hungarian: kommutátor
• Portuguese: comutador m
• (deprecated template usage) {{trans-mid}}
• Turkish: değişeç

binary function in a ring

• Swedish: kommutator (sv) c
• (deprecated template usage) {{trans-mid}}
• Turkish: değişeç

See also

• nilpotent group
• solvable group

Further reading

• Commutative property on Wikipedia.Wikipedia

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Latin

Verb

(deprecated template usage) commūtātor

1. second-person singular future passive imperative of commūtō
2. third-person singular future passive imperative of commūtō

References

• 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^[1], pre-publication website, 2005-2016