## completion of finitely generated module over non-Noetherian ring

Let $A$ be a commutative ring with unity and fix $f \in A$. Any $A$-module $M$ has its $f$-adic completion, the $\hat{A}$-module $\hat{M} = \underset{n}{\lim} M/f^nM$. There is a canonical map $\hat{A} \otimes_A M \to \hat{M}$, which is surjective if $M$ is finitely generated. My question is about additional conditions which imply that this map … Read more