\begin{definition}[Definition:Additive Function on UFD]
Let $R$ be a unique factorization domain.
Let $f : R \to \C$ be a complex-valued function.
Then $f$ is '''additive''' {{iff}}:
:For all coprime $x,y\in R$, $f(xy) = f(x) + f(y)$
\end{definition}