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This note extends certain results of Cartan-Eilenberg's Homological algebra, Chapter VII, Integral domains, to rings with one-sided field of quotients. Let R be a ring with a left field of quotients Q. We prove the following results. If A is a left P-module and tA the set of all its torsion elements then Torf(Q/R, A)=tA. With a slightly modified definition of inversible ideal it is proved that the notions of projective and inversible ideals are equivalent.If, in addition, R is left semihereditary then every finitely generated torsion-free right P-module is P-flat. Every finitely generated torsion-free left P-module can be imbedded in a finitely generated free left P-module if and only if R has both left and right field of quotients. Finally we give an example of a ring having a left field of quotients but not a right one. This implies that there exist finitely generated torsion-free left P-modules which cannot be imbedded in a projective left P-module.