\begin{definition}[Definition:Associate/Integral Domain/Definition 2]
Let $\struct {D, +, \circ}$ be an integral domain.
Let $x, y \in D$.
$x$ and $y$ are '''associates (in $D$)''' {{iff}}:
:$\ideal x = \ideal y$
where $\ideal x$ and $\ideal y$ denote the ideals generated by $x$ and $y$ respectively.
\end{definition}