Noetherian ring

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English[edit]

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Etymology[edit]

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

Pronunciation[edit]

  • IPA(key): /nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/

Noun[edit]

Noetherian ring (plural Noetherian rings)

  1. (mathematics, abstract algebra) A commutative ring in which every ideal is finitely generated.
  2. (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[edit]