zero divisor
zero divisor · zero divisors
An element a of a ring R for which there exists some nonzero element x ∈ R such that…An element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.
Meaning
2 sensesAn element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.
An idempotent element e#92;ne 1 of a ring is always a (two-sided) zero divisor, since e(1-e)#61;0#61;(1-e)e.
A nonzero element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.
Translations
1 languagesForms
plural: zero divisorsAntonyms
1 antonymsany element whose product with some nonzero element is zero:regular element