A ring \(R\) is called right PF if every faithful right \(R\)-module is a generator for the category of right \(R\)-modules. It is well-known that a ring \(R\) is right PF if and only if \(R\) is semiperfect and right self-injective with essential right socle. A module \(V\) is called local if it has a largest proper submodule, while a module \(W\) is called colocal if \(\text{Soc}(W)\) is simple and essential in \(W\).
The authors show that a ring \(R\) is right PF if and only if \(R_R\) has finite uniform dimension and every colocal, injective right \(R\)-module is projective. As a consequence a semiperfect ring \(R\) is right PF if and only if the injective hull of every simple right \(R\)-module is projective.