Noetherian ring

noun1

1. •
   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).

   • The central position occupied by Noetherian rings in commutative ring theory became evident from her^([Noether's]) work. — 1986