A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

A module M is called morphic if M/M α≅ ker (α) for all endomorphisms α in end (M), and a
ring R is called a left morphic ring if RR is a morphic module. We consider the open question …

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring
is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or …

Motivated by a result of Mochizuki [Mochizuki, H.(1965). Finitistic global dimension for rings.
Pacific J. Math. 15 (1): 249–258] that, for a left perfect ring R with Jacobson radical if and …

There are three outstanding conjectures about quasi-Frobenius rings: The Faith conjecture
that every left perfect, right selfinjective ring is quasi-Frobenius; The FGF-conjecture that …

A ring R is called a right WPF-ring (weak PF-ring) if R is a semiperfect right simple-injective
ring with essential right socle. The class of right WPF-rings is broader than that of right PF …

Let R be an arbitrary ring with identity and M be a right R-modulewith S= End (MR). Let f∈ S.
f is called π-morphic if M/fn (M)∼= r M (fn) for some positive integer n. A module M is called …

The Faith conjecture asserts that a semiprimary, right self-injective ring is quasi-Frobenius
(QF). This paper is a compendium of results (without proof) relating to the conjecture, usually …