English Dictionary

zero divisor

noun

(algebra, ring theory) An element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.

In algebra, a zero divisor is an element of a ring that multiplied by another element gives zero.

意味（1）

(algebra, ring theory) 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 ne 1 of a ring is always a (two-sided) zero divisor, since e(1-e)=0=(1-e)e.

意味（2）

(algebra, ring theory) 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[x] also has no zero divisors.