commutator background

commutator

/ˈkɑmjəteɪtər/ /ˈkɑməteɪtər/

Illustration commutator - Image 1

Illustration commutator - Image 2

noun

整流子

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. "

息子のおもちゃの車の小さなモーターには、電流を反転させる整流子があり、これにより車輪は同じ方向に回転し続けることができます。

electronics device machine electric technology

Illustration commutator - Image 1

noun

交換子

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. "

群論において、2つの要素の交換子は、それらの要素がどれだけ交換しないかを教えてくれます。交換子が単位元に等しい場合、要素は完全に交換します。

math group logic

Illustration commutator - Image 1

noun

交換子

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. "

抽象代数学において、交換子 [x, y] = xy - yx は、2つの要素 x と y がどの程度可換性に失敗するかを示しています。交換子がゼロの場合、x と y は完全に可換です。

math logic technical science system