Phrase guide

Noetherian ring

noun · 1 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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  • /nəˈtɛ.ɹi.ən ˈɹɪŋɡ/

1

noun

Meaning 1

A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated).

Definition source: English Wiktionary via Wiktextract

Qualifier: ring theory

Topics: algebra, mathematics, sciences

Examples

  • 2004, K. R. Goodearl, Introduction to the Second Edition, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 2nd Edition, page viii, During this same period, the explosive growth of the area of quantum groups provided a large new crop of noetherian rings to be analyzed, and thus gave major impetus to research in noetherian ring theory.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after German mathematician Emmy Noether (1882–1935).