Emmy Noether, who was the first to study the ascending and descending chain conditions for rings, and for whom the term is named.

In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending chain condition on certain kinds of subobjects; in particular,

Noetherian ring, a ring that satisfies the ascending chain condition on ideals.

Noetherian module, a module that satisfies the ascending chain condition on submodules.

Artinian ring, a ring that satisfies the descending chain condition on ideals.