\begin{definition}[Definition:Left Zero Divisor]
Let $\struct {R, +, \circ}$ 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 $R \setminus \set {0_R}$.
\end{definition}