Definition:Derivation on Ring

Definition
Let $R$ be a ring.

A derivation on $R$ is a group homomorphism $D$ of the additive group of $R$ which satsfies the Leibniz law:
 * $\forall a, b \in R: D \left({a b}\right) = D \left({a}\right) b + a D \left({b}\right)$

Also see

 * Definition:Differential Ring
 * Definition:Leibniz Law