WHEN IS A SEMIPERFECT RING RIGHT PF?

Abstract

It 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.