A note on M-projective modules. II (Q2266759)

The aim of this paper is to study a type of ''weakly'' M-projective modules, namely finitely M-projective modules; a left R-module P is said to be finitely M-projective, M being a fixed left R-module, iff for each epimorphism \(p: M\to M''\) with M'' an arbitrary finitely cogenerated left R-module and for each morphism \(f: P\to M''\) there exists a morphism \(h: P\to M\) such that \(f=ph\). The author gives sufficient conditions for a finitely M-projective module to be M-projective. Thus, it is proved that if P is a finitely M-projective module, \(S=End(_ RP)\), and the left S- module \(Hom_ R(P,M)\) is linearly compact, then P is M-projective.