# A projective module over a domain that is not faithfully flat?

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