Zero divisor

Symbol-free definition
An element in a (nonzero) commutative unital ring is termed a zero divisor if there exists a nonzero element with which its product is zero.

Definition with symbols
An element $$a$$ in a ring $$R$$ is termed a zero divisor if there exists a $$b \ne 0$$ such that $$ab = 0$$.

Stronger properties

 * Nilpotent element

Weaker properties

 * Non-invertible element