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Let $R$ be a Bezout domain, and $I$ any ideal inside of $R$. Is the $I$-adic completion $$ \varprojlim_i R/I^i $$ necessarily a Bezout domain? If not, what conditions (on $R$ or $I$) might ensure that it is a Bezout domain?

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    $\begingroup$ To start with, it is not necessarily a domain: if you take $R=\mathbb{Z}$ and $I=6\mathbb{Z}$, the completion is $\mathbb{Z}_2\times\mathbb{Z}_3$. $\endgroup$
    – Laurent Moret-Bailly
    Commented Jun 25, 2014 at 18:48

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