Definition:Associate/Integers

Definition

Let $x, y \in \Z$.

Then $x$ is an associate of $y$ if and only if they are both divisors of each other.

That is, $x$ and $y$ are associates if and only if $x \divides y$ and $y \divides x$.

Also known as

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

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $2$: Integers and natural numbers: $\S 2.2$: Divisibility and factorization in $\mathbf Z$