\begin{definition}[Definition:Completely Multiplicative Function]
Let $K$ be a field.
Let $f: K \to K$ be a function on $K$.
Then $f$ is described as '''completely multiplicative''' {{iff}}:
:$\forall m, n \in K: \map f {m n} = \map f m \map f n$
That is, a '''completely multiplicative function''' is one where the value of a product of two numbers equals the product of the value of each one individually.
\end{definition}