---
tag: 0670T59HGE
kind: concept
name: Noetherian ring
msc: ["13E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Noetherian_ring
    locator: lead section
same_as:
  wikidata: Q582271
  wikipedia: Noetherian ring
---

## Summary

A Noetherian ring is a ring in which every ideal is finitely generated, or equivalently, every increasing chain of ideals is eventually constant.
The [[definition of a Noetherian ring|0MVH4Y1CRZ]] gives the conditions.