zero divisor

名词 n.

中文释义

英文释义

名词 n.

An 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.

— If R is an integral domain, that is, has no zero divisors, then R#91;x#93; also has no zero divisors.

zero divisors plural zero-divisor alternative

反义词

regular element

下位词

trivial zero divisor exact zero divisor left zero divisor right zero divisor two-sided zero divisor

衍生词

zero divisor graph