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 $x, y \in R$: $\map f {x y} = \map f x + \map f y$

Also see

 * Definition:Multiplicative Function on UFD