\begin{definition}[Definition:Proper Divisor]
Let $\struct {D, +, \circ}$ be an integral domain whose zero is $0_D$ and whose unity is $1_D$.
Let $U$ be the group of units of $D$.
Let $x, y \in D$.
Then $x$ is a '''proper divisor''' of $y$ {{iff}}:
:$(1): \quad x \divides y$
:$(2): \quad y \nmid x$
:$(3): \quad x \notin U$
That is:
:$(1): \quad x$ is a divisor of $y$
:$(2): \quad x$ is not an associate of $y$
:$(3): \quad x$ is not a unit of $D$
\end{definition}