zero divisor

Noun

Meaning

(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
≠
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}

.

(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.

Antonyms

Close letter words and terms