Category:Definitions/Proper Divisors

This category contains definitions related to Proper Divisors.
Related results can be found in Category:Proper Divisors.

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 $y$ if and only if:

$(1): \quad x \divides y$

$(2): \quad y \nmid x$

$(3): \quad x \notin U$

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 $D$