Skip to main content
5 of 6
Edit: Removed the assumption of torsion-freeness since it was redundent.

A module that is projective and torsion-free but not faithfully flat?

Let $R$ be a (noncommutative) unital ring which is a domain and let $\mathcal{N}$ be a non-zero projective (right) module. Projectivity of course implies that $\mathcal{N}$ is flat, but does the fact that $R$ is also a domain imply that $\mathcal{N}$ is faithfully flat?