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The Stacks project

Lemma 10.82.5. Let $M$ be an $R$-module. Then $M$ is flat if and only if any exact sequence of $R$-modules

\[ 0 \to M_1 \to M_2 \to M \to 0 \]

is universally exact.

Proof. This follows from Lemma 10.81.3 and Theorem 10.82.3 (5). $\square$

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