Definition:Additive Function on UFD

Definition
Let $R$ be a unique factorization domain.

Let $f : R \to \C$ be a complex-valued function.

Then $f$ is additive :
 * For all coprime $x,y\in R$, $f(xy) = f(x) + f(y)$

Also see

 * Definition:Multiplicative Function on UFD
 * Definition:Additive Function (Number Theory)