A non-Noetherian local ring with finitely generated maximal ideal
Some time ago I found the following interesting lemma on the stacksproject:
Theorem: (tag/05GH) Let be a finitely generated ideal in a ring
. Then the
-adic completion
is Noetherian if
is.
Corollary: Let be a complete local ring with a finitely generated maximal ideal
. Then
is …