Definition:Associate/Integral Domain/Definition 2

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

Let $x,y \in D$.

Then $x$ and $y$ are associates iff:
 * $\left({ x }\right) = \left({ y }\right)$

where $\left({x}\right)$ and $\left({y}\right)$ denote the ideals generated by $x$ and $y$ respectively.

Also see

 * Equivalence of Definitions of Associates