 ##  [Noetherian Ring](/noetherian-ring) 

  ##  [Noetherian Ring](https://mathlogic.quantumdictionary.io/noetherian-ring-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A ring in which every ascending chain of ideals stabilizes (satisfies the ascending chain condition on ideals); equivalently, every ideal is finitely generated.

 
 ##  [Noetherian Ring](https://algebra.quantumdictionary.io/noetherian-ring-1) 

  
 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 
Definition

A ring in which every ascending chain of ideals stabilizes; equivalently every ideal is finitely generated.