Derivation (differential algebra)

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In mathematics, a derivation is a function on an algebra that generalizes certain features of the derivative operator. Specifically, given an algebra A {\displaystyle A} over a ring or a field K {\displaystyle K} , a K {\displaystyle K} -derivation is a K {\displaystyle K} -linear map D : A → A {\displaystyle D:A\to A} that satisfies Leibniz's law: D ( a b ) = a D ( b ) + D ( a ) b . {\displaystyle D(ab)=aD(b)+D(a)b.} The same definition generalizes word-for-word whenever M {\displaystyle M} is an...

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