The Stacks project

Lemma 10.93.5. Let $R$ be a Noetherian ring and let $M$ be a $R$-module. Suppose $M$ is a direct sum of countably generated $R$-modules, and suppose there is a universally injective map $M \to R[[t_1, \ldots , t_ n]]$ for some $n$. Then $M$ is projective.

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