# Definition:Associate/Integral Domain/Definition 3

## Definition

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

Let $x, y \in D$.

$x$ and $y$ are associates (in $D$) if and only if there exists a unit $u$ of $\struct {D, +, \circ}$ such that:

$y = u \circ x$

and consequently:

$x = u^{-1} \circ y$

That is, if and only if $x$ and $y$ are unit multiples of each other.

## Also see

• Results about associates can be found here.