For questions on Noetherian rings, Noetherian modules and related notions.

A (commutative) ring is called *Noetherian* if every ascending chain of ideals becomes stationary. For non-commutative rings, the notions of *left-* and *right-Noetherian* exist, and they apply to left and right ideals respectively. A Noetherian non-commutative ring is both left- and right-Noetherian.

More generally, a module is Noetherian if each ascending chain of submodules becomes stationary.

A vector space is Noetherian if and only if it is of finite dimension, and "Noetherian" can in a vague way be considered as a generalization of "finite-dimensional."