PROJECTIVE MODULES

. In this note we prove that if R is a ring satisfying a polynomial identity and P is a projective left .R-module such that P is finitely generated modulo the Jacobson radical, then P is finitely generated. As a corollary we get that if R is a ring still satisfying a polynomial identity and M is a finitely generated flat /R-module such that M/JM is ^//-projective, then M is R-projective, J denotes the Jacobson radical.