1.NounAn 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
≠
1
{\displaystyle e\neq 1}
of a ring is always a (two-sided) zero divisor, since
e
(
1
−
e
)
=
0
=
(
1
−
e
)
e
{\displaystyle e(1-e)=0=(1-e)e}
."
2.NounA nonzero element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.