Zero Divisor Definition

noun

(algebra ZERO DIVISOR 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.
Wiktionary

(algebra ZERO DIVISOR R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.

Wiktionary

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zero divisor