> [!NOTE] Definiton (Zero Divisor) > Let $(R,+,\times)$ be a [[Rings|ring]]. A zero divisor is an element $x\in R$ such that there exists $y\in R\setminus \{ 0_{R} \}$ such that $x \times y =0_{R}$or $y \times x = 0_{R}.$ > [!Example] > The [[Zero of Non-Zero Ring is a Zero Divisor|zero of a non-null ring is a zero divisor]]. # Properties A [[Proper Zero Divisor|proper zero divisor]] is zero divisor that is not $0_{R}.$ Zero divisor cannot be a unit.