Lemma 10.95.3. Let $R \to S$ be a faithfully flat ring map. Let $M$ be an $R$-module. If the $S$-module $M \otimes _ R S$ is countably generated and projective, then $M$ is countably generated and projective.
Lemma 10.95.3. Let $R \to S$ be a faithfully flat ring map. Let $M$ be an $R$-module. If the $S$-module $M \otimes _ R S$ is countably generated and projective, then $M$ is countably generated and projective.
Proof. Follows from Lemmas 10.83.2, 10.95.1, and 10.95.2 and Theorem 10.93.3. $\square$
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