Definition:Associate/Commutative and Unitary Ring

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Let $\struct {R, +, \circ}$ be a commutative ring with unity.

Let $x, y \in R$.

Then $x$ and $y$ are associates (in $R$) if and only if there exists a unit $u$ of $\struct {R, +, \circ}$ such that $u \circ x = y$.

Also known as

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