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?
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Edit: Removed the assumption of torsion-freeness since it was redundent.
Tim Montegue
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A module that is projective and torsion-free but not faithfully flat?
Tim Montegue
- 435
- 2
- 7