Definition:Associate/Integral Domain/Definition 1

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

Let $x, y \in D$.

Then $x$ and $y$ are associates iff they are both divisors of each other.

That is, $x$ is an associate of $y$ iff $x \mathop \backslash y$ and $y \mathop \backslash x$.

Also see

 * Equivalence of Definitions of Associates