(algebra) Of a ring in which any ascending chain of ideals eventually starts repeating. / (algebra) Of a module in which any ascending chain of submodules eventually starts repeating.

Alternative letter-case form of noetherian

The condition of being noetherian

(algebra, ring theory) A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated).

A Noetherian ring which is also an integral domain.

plural of Noetherian domain

plural of Noetherian ring

Alternative letter-case form of Noetherian module

(algebra) A module whose every submodule is finitely generated; or equivalently, a module whose submodules satisfy an ascending chain condition (i.e., any ascending chain of submodules levels off after a finite number of steps).