noetherian

Meanings

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;

1. Alternative letter-case form of noetherian.

Etymology

From Emmy Noether.

Translations