3
$\begingroup$

Let $A$ be a commutative local ring with maximal ideal $m$ and $\hat{A}$ be its $m$-adic completion. Are there any non-trivial conditions on $A$, under which $\hat{A}$ noetherian implies $A$ noetherian?

Improve this question
$\endgroup$
1
  • $\begingroup$ As a remark, the $m$-adic completion might not be $m$-adically complete. $\endgroup$
    – Z. M
    Commented Mar 5, 2022 at 22:34

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .