Thuses

Math discussions

Category: commutative algebra

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

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