# Definition:Associate/Integral Domain/Definition 1

## Definition

Let $\struct {D, +, \circ}$ be an integral domain.

Let $x, y \in D$.

$x$ is an associate of $y$ (in $D$) if and only if they are both divisors of each other.

That is, $x$ and $y$ are associates (in $D$) if and only if $x \divides y$ and $y \divides x$.