nLab divisor (ring theory)

Definitions

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.

Related concepts

• zero divisor

• divisor (algebraic geometry)

See also

• Wikipedia, Divisibility (ring theory)