Corollary 2

Let $A$ be a commutative Noetherian ring, $m$ an ideal of $A$ and $\hat{A}$ the Hausdorff completion of $A$ with respect to the $m$-adic topology. If an element $a \in A$ is not a divisor of 0 in $A$, its canonical image $a'$ in $\hat{A}$ is not a divisor of 0 in $\hat{A}$.

As $\hat{A}$ is a flat $A$-module, the corollary is a special case of Chapter I, § 2, no. 4, Proposition 3 (i).