 Derivation of an algebra

For an $A$-algebra $B$ and a $B$-module $M$, an $A$-linear derivation is an additive map $D:B\to M$ satisfying $D(a)=0$ for $a\in A$ and the Leibniz rule $D(b{b}^{\prime })=bD(b^{\prime })+b^{\prime }D(b)$.