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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 I be a finitely generated ideal in a ring R. Then the I-adic completion \widehat{R} is noetherian if so is R/I.

Corollary: Let R be a complete local ring with a finitely generated maximal ideal \mathfrak{m}. Then R is noetherian.

This corollary turns out to be actually …