## Non-noetherian local ring with finitely generated maximal ideal

Some time ago I found the following interesting lemma on the stackproject:

**Theorem:** (tag/05GH) Let be a finitely generated ideal in a ring . Then the -adic completion is noetherian if so is .

**Corollary:** Let be a complete local ring with a finitely generated maximal ideal . Then is noetherian.

This corollary turns out to be actually …