\begin{definition}[Definition:Multiplicative Function on Ring]
Let $\struct {R, +, \circ}$ be a ring.
Let $f: R \to \R$ be a (real-valued) function on $R$.
$f$ is a '''multiplicative function on $R$''' {{iff}}:
:$\forall x, y \in R: \map f {x \circ y} = \map f x \times \map f y$
That is, a '''multiplicative function on $R$''' is one where the value of the product of two elements of $R$ equals the product of their values.
\end{definition}