# nLab divisor (ring theory)

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## 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.