I am working through a proof somewhere, and I want to use this:
Let $(R,\mathfrak m)$ be a local ring (Noetherian commutative) and let $M$ be an $R$-module. If $\mathfrak p$ is an associated prime of $M$, then there exists $\hat{\mathfrak p}$, an associated prime of $M \otimes_R \hat{R}$ such that $\hat{\mathfrak p} \cap R = \mathfrak p$, where $\hat{R}$ denotes the $\mathfrak m$-adic completion of $R$.
Is this the case?