derivation (original) (raw)

Let R be a commutative ring. A derivation d on an R-algebra A into an A-module M is an R-linear transformation d:A→M satisfying the properties

• •
  d⁢(a⁢𝐱+b⁢𝐲)=a⁢d⁢𝐱+b⁢d⁢𝐲
• •
  d⁢(𝐱⋅𝐲)=𝐱⋅d⁢𝐲+d⁢𝐱⋅𝐲

for all a,b∈R and 𝐱,𝐲∈A.