# Flat not projective, projective not free [duplicate]

I am looking for examples of a flat but not projective module, and of a projective but not free module.

-

## marked as duplicate by rschwieb, Did, Micah, Erick Wong, AmzotiMar 20 '13 at 14:25

The rational numbers are a flat but not projective $\mathbb Z$-module.
$\mathbb Z\oplus 0$ is a projective but not free $\mathbb Z\oplus \mathbb Z$-module.