# Definition:Left Zero Divisor

## Definition

Let $\left({R, +, \circ}\right)$ be a ring.

A left zero divisor (in $R$) is an element $x \in R$ such that:

$\exists y \in R^*: x \circ y = 0_R$

where $R^*$ is defined as $R \setminus \left\{{0_R}\right\}$.