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

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

Answer

Attribution
Source : Link , Question Author : Tim Montegue , Answer Author : Community

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