principal ideal ring

noun

A commutative ring in which every ideal is a principal ideal.

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

nounprincipal ideal ring (plural principal ideal rings)

plural principal ideal rings

  1. ring theoryalgebraA commutative ring in which every ideal is a principal ideal.
  2. ring theoryalgebraA noncommutative ring in which every left ideal is a principal ideal and so is every right ideal.

Synonyms & antonyms

Narrower
principal ideal domain
Cite this entry
APA

principal ideal ring. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/principal%20ideal%20ring

MLA

“principal ideal ring.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/principal%20ideal%20ring. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “principal ideal ring,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/principal%20ideal%20ring.

Source: principal ideal ring on Wiktionary, CC BY-SA 4.0.