nLab divisor (ring theory)

Redirected from "divisibility relation".

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Let $R$ be a commutative ring (or any ring).

An element $x$ of $R$ is a divisor of an element $y$ of $R$ if there exists an element $z$ of $R$ such that $z x = y$ .

If $R$ is (or may be) non-commutative, then we may distinguish left and right divisors in the usual way.