Exercise 111.5.1 (02CQ)—The Stacks project

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Exercise 111.5.1. Let $S$ be a multiplicative subset of the ring $A$ .

For an $A$ -module $M$ show that $S^{-1}M = S^{-1}A \otimes _ A M$ .
Show that $S^{-1}A$ is flat over $A$ .

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