Zero Divisor
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
In a ring R, a nonzero element a is a zero divisor if there exists a nonzero b with a·b = 0 or b·a = 0. In commutative rings the two notions coincide; in noncommutative rings one distinguishes left and right zero divisors.
Zero Divisor
- Pure Mathematics -
Algebra Dictionary
Definition
A nonzero element a in a ring R such that there exists a nonzero b in R with ab = 0; zero divisors obstruct cancellation and prevent R from being an integral domain.