Definition:Proper Divisor

Definition
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 $y$ :


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

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 $D$

Integers
As the set of integers form an integral domain, the concept of a proper divisor is fully applicable to the integers.

Also see

 * Definition:Aliquot Part
 * Definition:Aliquant Part