Banh Duc DungLe Duc ThoangNguyen Van SanhUniversity of Transport in Hochiminh CityPhu Yen UniversityMahidol University2018-07-122018-07-122008-09-01Asian-European Journal of Mathematics. Vol.1, No.3 (2008), 353-35817937183179355712-s2.0-84857562717https://repository.li.mahidol.ac.th/handle/20.500.14594/19415It is well-known that a ring R is right PF if and only if it is semiperfect and right self-injective with essential right socle. In this note, it is shown that a ring R is right PF if and only if u.dim(RR) < ∞ and every colocal, injective right R-module is projective. Consequently, a semiperfect ring R is right PF if and only if the two classes of colocal injective right R-modules and local projective right modules coincide. © 2008 World Scientific Publishing Company.Mahidol UniversityMathematicsArticleSCOPUS10.1142/S1793557108000308