English

Noun

Noetherian ring ‎(plural Noetherian rings)

1. (mathematics, abstract algebra) A commutative ring in which every ideal is finitely generated.
2. (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

• Noetherian domain
  • Dedekind domain
• Artinian ring