Definition:Multiplicative Function on UFD

Definition
Let $R$ be a unique factorization domain.

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

Then $f$ is multiplicative :
 * For all coprime $x, y\in R$: $f \left({x y}\right) = f \left({x}\right) f \left({y}\right)$

Also see

 * Definition:Additive Function on UFD