Definition of "noetherian"

noetherian

/noʊˈθɪəriən/

adjective
not comparable
1. (algebra) Satisfying some (usually ascending) chain condition:
  1. (of a ring) In which any ascending chain of ideals eventually becomes constant.
  2. (of a module) In which any ascending chain of submodules eventually becomes constant.
  3. (of a group) In which any ascending chain of subgroups eventually becomes constant.
  4. (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 Spec ⁡ A i , where each A i is a noetherian ring;