Word.ws English Dictionary

zero divisors

zero divisors is the plural of zero divisor.

Meaning of zero divisor

Noun

zero divisor (plural zero divisors)

  1. (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#92;ne 1 of a ring is always a (two-sided) zero divisor, since e(1-e)#61;0#61;(1-e)e.
  2. (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#91;x#93; also has no zero divisors.2000, Lindsay N. Childs, A Concrete Introduction to Higher Algebra, 2nd edition, Springer, page 234

Questions about zero divisors

What is zero divisors the plural of?
Zero divisors is the plural of zero divisor.

Words near zero divisors in the dictionary

  1. zero derive
  2. zero derived
  3. zero derives
  4. zero deriving
  5. zero divisor
  6. zero divisors
  7. zero ending
  8. zero endings
  9. zero fighter
  10. zero fighters
  11. zero fucks given

Source and license

Adapted from Wiktionary: zero divisors (page history and authors); zero divisor (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “zero divisors.” Word.ws, https://word.ws/zero_divisors. Based on Wiktionary, CC BY-SA 4.0.