Definition:Zero Divisor/Commutative Ring

Definition
Let $\struct {R, +, \circ}$ be a commutative ring.

A 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 $R \setminus \set {0_R}$.

The expression:
 * $x$ is a zero divisor

can be written:
 * $x \divides 0_R$

Also see

 * Definition:Proper Zero Divisor