noetherian

See also: Noetherian

English

Alternative forms

• Noetherian

Etymology

From Emmy Noether.

Pronunciation

IPA^(key): /noʊˈθɪəriən/

Adjective

noetherian (not comparable)

1. (algebra) Satisfying some (usually ascending) chain condition:
   2. (of a ring) In which any ascending chain of ideals eventually becomes constant.
   3. (of a module) In which any ascending chain of submodules eventually becomes constant.
   4. (of a group) In which any ascending chain of subgroups eventually becomes constant.
   5. (of a topological space) In which any ascending chain of open subsets eventually becomes constant.
2. (mathematics, of a binary relation on a set) Such that the converse relation is well-founded (on that set).
3. (algebraic geometry, of a scheme) admitting a finite covering by open affine subsets $\operatorname {Spec} A_{i}$, where each $A_{i}$ is a noetherian ring;

Derived terms

• noetherian module

 

Translations

math

• Basque: noetherdar
• Chinese:

  Mandarin: 诺特的

• French: noethérien (fr)
• Italian: noetheriano

See also

• Artinian
• ascending chain condition