Is this true that finitely generated flat module over an integral domain is projective.
If Yes, please provide a proof.



On Flat and Projective Modules over integral domain
Yes, this is true. Lemma 5 on page 249 of Cartier, "Questions de rationalité des diviseurs en géométrie algébrique" says that over an integral domain, whether or not it is Noetherian, if the localisation of a finitely generated module at every maximal ideal is free, then the module is projective. Over a local ring, every finitely generated flat module is free (see for example Matsumura, "Commutative Ring Theory" Theorem 7.10). Putting these together gives you a positive answer to your question.


