Word.ws English Dictionary

Noetherian ring

/nəˈtɛ.ɹi.ən ˈɹɪŋɡ/

Noetherian ring noun: 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).

Noun

Noetherian ring (plural Noetherian rings)

  1. (ring theory) 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).
    • The central position occupied by Noetherian rings in commutative ring theory became evident from her^([Noether's]) work.1986, Hideyuki Matsumura, translated by M. Reid, Commutative Ring Theory, Paperback edition, Cambridge University Press, published 1989, page ix
    • In this chapter the focus moves from semiprime rings to general Noetherian rings, although it does concentrate on prime and semiprime ideals.2000, John C. McConnell, James Christopher Robson, Lance W. Small, Noncommutative Noetherian Rings, 2nd edition, American Mathematical Society, page 97

Noetherian ring meaning in Tamil

Noetherian ring in Tamil

நோதிரிய வளையம்

Forms of Noetherian ring

pluralNoetherian rings
alternative formnoetherian ring

Origin of Noetherian ring

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

Words formed from Noetherian ring

  • left Noetherian ring
  • right Noetherian ring

Questions about Noetherian ring

What does Noetherian ring mean?
Noetherian ring means 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).
What is Noetherian ring in Tamil?
Noetherian ring in Tamil is நோதிரிய வளையம். See Noetherian ring meaning in Tamil.
What part of speech is Noetherian ring?
Noetherian ring is a noun.
How do you pronounce Noetherian ring?
Noetherian ring is pronounced /nəˈtɛ.ɹi.ən ˈɹɪŋɡ/.
What is the plural of Noetherian ring?
The plural of Noetherian ring is Noetherian rings.

Words near Noetherian ring in the dictionary

  1. noetherian
  2. Noetherian domain
  3. Noetherian domains
  4. noetherian module
  5. noetherian modules
  6. Noetherian ring
  7. Noetherian rings
  8. noetherianity
  9. Noetian
  10. Noetians
  11. noetic

Source and license

Adapted from Wiktionary: Noetherian ring (page history and authors); noetherian ring (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “Noetherian ring.” Word.ws, https://word.ws/noetherian_ring. Based on Wiktionary, CC BY-SA 4.0.