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