Lemma 10.148.3. Let $R \to S$ be a ring map. The following are equivalent:

$R \to S$ is formally unramified,

$R \to S_{\mathfrak q}$ is formally unramified for all primes $\mathfrak q$ of $S$, and

$R_{\mathfrak p} \to S_{\mathfrak q}$ is formally unramified for all primes $\mathfrak q$ of $S$ with $\mathfrak p = R \cap \mathfrak q$.

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