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单词 ZeroDivisor
释义

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).

Titlezero divisor
Canonical nameZeroDivisor
Date of creation2013-03-22 12:49:59
Last modified on2013-03-22 12:49:59
Ownercvalente (11260)
Last modified bycvalente (11260)
Numerical id9
Authorcvalente (11260)
Entry typeDefinition
Classificationmsc 13G05
Related topicCancellationRing
Related topicIntegralDomain
Related topicUnity
Definesleft zero divisor
Definesright zero divisor
Definesregular element
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更新时间:2025/5/4 13:21:06