Definition:Zero Divisor/Also defined as

Zero Divisor: Also defined as
Some sources define a zero divisor as an element $x \in R_{\ne 0_R}$ such that:
 * $\exists y \in R_{\ne 0_R}: x \circ y = 0_R$

where $R_{\ne 0_R}$ is defined as $R \setminus \set {0_R}$.

That is, the element $0_R$ itself is not classified as a zero divisor.

This definition is the same as the one given on this website as a proper zero divisor.