The Stacks project

Lemma 10.148.4. Let $A \to B$ be a formally unramified ring map.

  1. For $S \subset A$ a multiplicative subset, $S^{-1}A \to S^{-1}B$ is formally unramified.

  2. For $S \subset B$ a multiplicative subset, $A \to S^{-1}B$ is formally unramified.

Proof. Follows from Lemma 10.148.3. (You can also deduce it from Lemma 10.148.2 combined with Lemma 10.131.8.) $\square$

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