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The Stacks project

Lemma 10.93.4. Let f: M \to N be universally injective map of R-modules. Suppose M is a direct sum of countably generated R-modules, and suppose N is flat and Mittag-Leffler. Then M is projective.

Proof. By Lemmas 10.82.7 and 10.89.7, M is flat and Mittag-Leffler, so the conclusion follows from Theorem 10.93.3. \square


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