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 $D$) there exists a unit $u$ of $\struct {D, +, \circ}$ such that:
 * $y = u \circ x = y$

and consequently:
 * $x = u^{-1} \circ y$

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

Also see

 * Equivalence of Definitions of Associate in Integral Domain