Theorem 10.85.4 (0593)—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
Theorem 10.85.4 (cite)

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Projective modules over local rings are free.

Theorem 10.85.4. If $P$ is a projective module over a local ring $R$ , then $P$ is free.

Proof. Follows from Lemmas 10.85.1, 10.85.2, and 10.85.3. $\square$

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Comment #1037 by Adeel Khan on September 15, 2014 at 08:10

Suggested slogan: Projective modules over local rings are free.

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