noetherian

adjective7

1. •
   Satisfying some (usually ascending) chain condition.
2. •
   In which any ascending chain of ideals eventually becomes constant.
3. •
   In which any ascending chain of submodules eventually becomes constant.
4. •
   In which any ascending chain of subgroups eventually becomes constant.
5. •
   In which any ascending chain of open subsets eventually becomes constant.
6. •
   Such that the converse relation is well-founded (on that set).
7. •
   admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;