We show that a semiperfect right FPF-ring is right self-injective if and only if J(R) — Z(RR), extending a well-known result due to Carl Faith on semiperfect right FPF-rings with nil Jacobson radical.

We give a characterization of reflexive modules over QF-3 rings generalizing the concept of linearly compact modules. Further, we study necessary and sufficient conditions for left QF-3 rings to be right QF-3.

It is shown that a two-sided continuous ring with ascending chain condition on left annihilators is quasi-Frobenius.

A ring R is said to be generated by faithful right cyclics (right finitely pseudo-Frobenius), denoted by GFC (FPF), if every faithful cyclic (finitely generated) right R-module generates the category of right R-modules. The class of right GFC rings includes right FPF rings, commutative rings (thus every ring has a GFC subring - its center), strongly regular rings, and continuous regular rings of bounded index. Our main results are: (1) a decomposition of a semi-prime quasi-Baer right GFC ring (e.g., a semiprime right FPF ring) is achieved by considering the set of nilpotent elements and the centrality of idempotnents; (2) a generalization of S. Page's decomposition theorem for a right FPF ring.