Lemma 10.85.1 (0590)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.85: Projective modules over a local ring
Lemma 10.85.1 (cite)

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Lemma 10.85.1. Let $R$ be a ring. Then every projective $R$ -module is free if and only if every countably generated projective $R$ -module is free.

Proof. Follows immediately from Theorem 10.84.5. $\square$

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