# Noetherian ring

## English[edit]

### Etymology[edit]

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

### Pronunciation[edit]

- IPA
^{(key)}: /nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/

### Noun[edit]

**Noetherian ring** (*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.