Definition 10.130.1. Let $\varphi : R \to S$ be a ring map and let $M$ be an $S$-module. A *derivation*, or more precisely an *$R$-derivation* into $M$ is a map $D : S \to M$ which is additive, annihilates elements of $\varphi (R)$, and satisfies the *Leibniz rule*: $D(ab) = aD(b) + bD(a)$.

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## Comments (2)

Comment #1849 by Peter Johnson on

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