Phrase guide

principal ideal ring

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Qualifier: ring theory

Topics: algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

A noncommutative ring in which every left ideal is a principal ideal and so is every right ideal.

Definition source: English Wiktionary via Wiktextract

Qualifier: ring theory

Topics: algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.