Let $\hat{R}$ is $m$-adic completion of a local ring $(R,m)$.What is the relation between $Min R$ and $Min \hat{R}$. we know that $\hat{R}$ is faithfully flat $R$-module. $Min R$=set of all minimal prime divisors of zero. I think

$p\in Min(R)$ iff $\hat{p}=p\hat{R}\in Min\hat{R}$.