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:

$\forall a, b \in R: \map D {a b} = \map D a b + a \map D b$

Also see

• Definition:Differential Ring
• Definition:Leibniz Law