Dictionary

noetherian en · ADJ

Pronunciation

• (US) audio
• /noʊˈθɪəriən/

Etymology

From Emmy Noether.

Meanings

1. (not-comparable, of a ring) Satisfying some (usually ascending) chain condition: ▸ In which any ascending chain of ideals eventually becomes constant.
2. (not-comparable, of a module) Satisfying some (usually ascending) chain condition: ▸ In which any ascending chain of submodules eventually becomes constant.
3. (not-comparable, of a group) Satisfying some (usually ascending) chain condition: ▸ In which any ascending chain of subgroups eventually becomes constant.
4. (not-comparable, of a topological space) Satisfying some (usually ascending) chain condition: ▸ In which any ascending chain of open subsets eventually becomes constant.
5. (not-comparable, of a binary relation on a set) Such that the converse relation is well-founded (on that set).
6. (not-comparable, of a scheme) admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;

Forms

Deriveds

noetherian module

Relateds

Artinian · ascending chain condition

Translations (4)

fr noethérien (math) · it noetheriano (math) · cmn 诺特的 (math) · eu noetherdar (math)