View source for Noetherian

{{also|Noetherian}}
==English==

===Alternative forms===
* {{l|en|Noetherian}}

===Etymology===
From [[w:Emmy Noether|Emmy Noether]].

===Pronunciation===
{{IPA|en|/noʊˈθɪəriən/}}
* {{audio|en|LL-Q1860 (eng)-Flame, not lame-noetherian.wav|a=US}}

===Adjective===
{{en-adj|-}}

# {{lb|en|algebra}} Satisfying some (usually [[ascending]]) {{w|Ascending chain condition|chain condition}}:
## {{senseid|en|ring}}{{lb|en|of a [[ring]]}} In which any ascending chain of [[ideal]]s eventually becomes constant.
## {{lb|en|of a [[module]]}} In which any ascending chain of [[submodule]]s eventually becomes constant.
## {{lb|en|of a [[group]]}} In which any ascending chain of [[subgroup]]s eventually becomes constant.
## {{lb|en|of a [[topological space]]}} In which any ascending chain of [[open]] [[subset]]s eventually becomes constant.
# {{lb|en|mathematics|of a [[binary relation]] on a [[set]]}} Such that the [[converse relation]] is [[well-founded]] (on that set).
# {{lb|en|algebraic geometry|of a [[scheme]]}} [[admit|admitting]] a [[finite]] covering by open [[affine]] subsets <math>\operatorname{Spec}A_i</math>, where each <math>A_i</math> is a {{l|en|noetherian|noetherian ring|id=ring}};

====Derived terms====
{{col2|en|noetherian module}}

====Translations====
{{trans-top|math}}
* Basque: {{t|eu|noetherdar}}
* Chinese:
*: Mandarin: {{t|cmn|诺特的}}
* French: {{t+|fr|noethérien}}
* Italian: {{t|it|noetheriano}}
{{trans-bottom}}

===See also===
* {{l|en|Artinian}}
* {{l|en|ascending chain condition}}

{{cln|en|eponyms}}
{{C|en|Mathematics}}