zero divisor

Let a be a nonzero element of a ring R.

The element a is a left zero divisor if there exists a nonzero element bR such that ab=0. Similarly, a is a right zero divisor if there exists a nonzero element cR such that ca=0.

The element a is said to be a zero divisor if it is both a left and right zero divisor. A nonzero element aR is said to be a regular elementPlanetmathPlanetmath if it is neither a left nor a right zero divisor.

Example: Let R=6. Then the elements 2 and 3 are zero divisors, since 2360(mod6).

Title zero divisor
Canonical name ZeroDivisor
Date of creation 2013-03-22 12:49:59
Last modified on 2013-03-22 12:49:59
Owner cvalente (11260)
Last modified by cvalente (11260)
Numerical id 9
Author cvalente (11260)
Entry type Definition
Classification msc 13G05
Related topic CancellationRing
Related topic IntegralDomain
Related topic Unity
Defines left zero divisor
Defines right zero divisor
Defines regular element