Definition:Associate/Commutative and Unitary Ring

Definition
Let $\left({R, +, \circ}\right)$ be a commutative ring.

Let $x, y \in R$.

Then $x$ and $y$ are associates iff there exists a unit $u$ of $\left({R, +, \circ}\right)$ such that $u x = y$.

Also known as
The statement $x$ is an associate of $y$ can be expressed as $x$ is associated to $y$.

Also see

 * Equivalence of Definitions of Associates