Noetherian ring

English

Etymology

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

Pronunciation

IPA^(key): /nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/

Noun

Noetherian ring (plural Noetherian rings)

(mathematics, abstract algebra) A commutative ring in which every ideal is finitely generated.
(mathematics, abstract algebra) A noncommutative ring which is both left-Noetherian and right-Noetherian, i.e., in which every left ideal is finitely generated and in which every right ideal is finitely generated, respectively.

Hyponyms

Noetherian domain
- Dedekind domain
Artinian ring

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