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 right FPF if each faithful finitely generated right R module is a generator of MOD-
R. The purpose of this paper is to answer several questions posed by C. Faith and S. Page …

Harada calls a ring $ R $ right simple-injective if every $ R $-homomorphism with simple
image from a right ideal of $ R $ to $ R $ is given by left multiplication by an element of $ R …

A left FPF ring is a ring R such that every finitely generated faithful left R-module generates
the category of left R-modules. It is shown that such rings split into R= A⊕ B, where A is a …

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 …

A ring R is called right FP-injective if every R-homomor-phism from a finitely generated
submodule of a free right R-module F into R extends to F. In this paper a ring R will be called …

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 …

A ring R is right finitely pseudo Frobenius (FPF) if every finitely generated faithful right jR-
module generates the category of right jR-modules. In [2], C. Faith has shown that a …

ON SEMIPERFECT FPF-RINGS Page 1 Canad. Math. Bull. Vol. 37 (2), 1994 pp. 287-288 ON
SEMIPERFECT FPF-RINGS MOHAMED YOUSIF ABSTRACT. We show that a semiperfect right …

A well known result of B. Osofsky asserts that if R is a left (or right) perfect, left and right
selfinjective ring thenR is quasi-Frobenius. It was subsequently conjectured by Carl Faith …