# Definition:Associate/Integers

< Definition:Associate(Redirected from Definition:Associate of Integer)

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## 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 $\mathbf Z$