English Dictionary

Noetherian ring

/nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/

noun

(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 is a commutative ring in which every non-empty set of ideals has a maximal element.

意味（1）

(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).

The central position occupied by Noetherian rings in commutative ring theory became evident from her work.