Lemma 115.4.9. If $R \to S$ is a faithfully flat ring map then for every $R$-module $M$ the map $M \to S \otimes _ R M$, $x \mapsto 1 \otimes x$ is injective.

**Proof.**
This lemma is a duplicate of Algebra, Lemma 10.82.11.
$\square$

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