derivation

Let $R$ be a commutative ring. A derivation $d$ on an $R$-algebra $A$ into an $A$-module $M$ is an $R$-linear transformation $\mathrm{d}:A\to M$ satisfying the properties

• $\mathrm{d}(a𝐱+b𝐲)=a\mathrm{d}𝐱+b\mathrm{d}𝐲$

• $\mathrm{d}(𝐱\cdot 𝐲)=𝐱\cdot \mathrm{d}𝐲+\mathrm{d}𝐱\cdot 𝐲$

for all $a,b\in R$ and $𝐱,𝐲\in A$.