Definition:Associate/Integral Domain/Definition 2

Definition
Let $\left({D, +, \circ}\right)$ be an integral domain.

Let $x,y \in D$.

We say that $x$ and $y$ are associates if $\left({ x }\right) = \left({ y }\right)$, where $\left({ x }\right)$ and $\left({ y }\right)$ denote the ideals generated by $x$ and $y$ respectively.

Also see

 * Equivalence of Definitions of Associates