> [!NOTE] Definition (Proper Zero Divisor) > Let $(R,+,\times)$ be a [[Rings|ring]]. A proper zero divisor is an element $x\in R\setminus \{0_{R} \}$ such that there exists $y\in R\setminus \{ 0_{R} \}$ with $x \times y =0_{R}$ > >That is, it is a [[Zero Divisor|zero divisor]] that is not $0_{R}.$ # Properties # Application An [[Integral Domain|integral domain]] is a non-null commutative ring with unity without proper zero divisors.