Zero divisor

Definition

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 $b\neq 0$ such that $ab=0$.

Relation with other properties

Stronger properties

• Nilpotent element

Weaker properties

• Non-invertible element