## noetherian-ring

Noun

(*plural* Noetherian rings)

- (mathematics, abstract algebra) A commutative ring in which every ideal is finitely generated.
- (mathematics, abstract algebra) A noncommutative ring which is both
*left-Noetherian*and*right-Noetherian*, i.e., in which every left ideal is finitely generated and in which every right ideal is finitely generated, respectively.

Hyponyms Artinian ring

Origin

Named after Emmy Noether (1882–1935), German mathematician.