Theorem 10.84.5. If $P$ is a projective $R$-module, then $P$ is a direct sum of countably generated projective $R$-modules.

** Any projective module is a direct sum of countably generated projective modules. **

**Proof.**
A module is projective if and only if it is a direct summand of a free module, so this follows from Theorem 10.84.4.
$\square$

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## Comments (1)

Comment #1337 by Hua Wang on

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