Definitions
1.AdjectiveSatisfying some (usually ascending) chain condition:
In which any ascending chain of ideals eventually becomes constant.
In which any ascending chain of submodules eventually becomes constant.
In which any ascending chain of subgroups eventually becomes constant.
In which any ascending chain of open subsets eventually becomes constant.
2.AdjectiveIn which any ascending chain of ideals eventually becomes constant.
3.AdjectiveIn which any ascending chain of submodules eventually becomes constant.
4.AdjectiveIn which any ascending chain of subgroups eventually becomes constant.
5.AdjectiveIn which any ascending chain of open subsets eventually becomes constant.
6.AdjectiveSuch that the converse relation is well-founded (on that set).
7.Adjectiveadmitting a finite covering by open affine subsets
Spec
A
i
{\displaystyle \operatorname {Spec} A_{i}}
, where each
A
i
{\displaystyle A_{i}}
is a noetherian ring;