Definition:Associate/Integral Domain/Definition 2

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

Let $x, y \in D$.

$x$ and $y$ are associates (in $D$) :
 * $\ideal x = \ideal y$

where $\ideal x$ and $\ideal y$ denote the ideals generated by $x$ and $y$ respectively.

Also see

 * Equivalence of Definitions of Associate in Integral Domain