commutator background

commutator

/ˈkɑmjəteɪtər/ /ˈkɑməteɪtər/

Illustration commutator - Image 1

Illustration commutator - Image 2

noun

Kommutator

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

Examples :

"The small motor in my son's toy car has a commutator that flips the current, allowing the wheels to keep spinning in the same direction. "

Der kleine Motor in dem Spielzeugauto meines Sohnes hat einen Kommutator, der den Strom umkehrt, wodurch sich die Räder in der gleichen Richtung weiterdrehen können.

electronics device machine electric technology

Illustration commutator - Image 1

noun

Kommutator

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.

Examples :

"In group theory, the commutator of two elements tells us how much those elements fail to commute; if the commutator equals the identity element, then the elements commute perfectly. "

In der Gruppentheorie zeigt uns der Kommutator zweier Elemente, wie stark diese Elemente nicht kommutieren; wenn der Kommutator dem Identitätselement entspricht, dann kommutieren die Elemente perfekt.

math group logic

Illustration commutator - Image 1

noun

Kommutator

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.

Examples :

"In abstract algebra, the commutator [x, y] = xy - yx shows us how much two elements x and y fail to commute; if the commutator equals zero, then x and y commute perfectly. "

In der abstrakten Algebra zeigt uns der Kommutator [x, y] = xy - yx, wie stark zwei Elemente x und y nicht kommutieren; wenn der Kommutator gleich Null ist, kommutieren x und y perfekt.

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