ABSTRACT
Definition 7.1.1 If A is an algebra over a commutative ring with identity R, then a mapping D : A → A is a derivation if for all a 1, a 2 ∈ A and r ∈ R,
D(a 1 + a 2) = D(a 1) + D(a 2),
D(r · a 1) = r · D(a 1), and
D(a 1 · a 2) = D(a 1) · a 2 + a 1 · D(a 2).
