Word.ws English Dictionary

reduced rings

reduced rings is the plural of reduced ring.

Meaning of reduced ring

Noun

reduced ring (plural reduced rings)

  1. (ring theory) A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.
    • We do this for reduced rings in Corollary 10, and for rings with nonzero nilpotents in Corollary 15.1997, Thomas G. Lucas, “Characterizing When R(X) is Completely Integrally Closed”, in Daniel Anderson, editor, Factorization in Integral Domains, Marcel Dekker, page 401

Questions about reduced rings

What is reduced rings the plural of?
Reduced rings is the plural of reduced ring.

Words near reduced rings in the dictionary

  1. reduced circumstances
  2. reduced isolation
  3. reduced mass
  4. reduced masses
  5. reduced ring
  6. reduced rings
  7. reduced row echelon form
  8. reduced row echelon forms
  9. reduced someone to tears
  10. reduced time
  11. reduced vowel

Source and license

Adapted from Wiktionary: reduced rings (page history and authors); reduced ring (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.

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