Definition:Associate

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

If two elements of $D$ are both divisors of each other, then they are called associates.

That is, if $x \backslash y$ and $y \backslash x$, then $x$ is an associate of $y$.

Notation
The notation $x \cong y$ is sometimes seen to indicate that $x$ is an associate of $y$.

Alternative Definition
Some sources define this concept on any commutative ring with unity $\left({R, +, \circ}\right)$:


 * $x$ and $y$ are associates if $u$ is an invertible element of $\left({R, \circ}\right)$ such that $u x = y$.