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 $$u x = y$$.