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?
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asked Mar 4, 2022 at 23:37
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$\begingroup$ As a remark, the $m$-adic completion might not be $m$-adically complete. $\endgroup$– Z. MMar 5, 2022 at 22:34
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