Definition:Proper Divisor

Definition
Let $\left({D, +, \circ}\right)$ 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:


 * $(1): \quad x \mathop \backslash y$
 * $(2): \quad y \nmid x$
 * $(3): \quad x \notin U$

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 $D$

Also known as
If $x \mathop \backslash y$, then $x$ may also be referred to as an aliquot part of $y$.

If $x \nmid y$, then $x$ may be referred to as an aliquant part.