Since Thrall [25] proposed the concept of QF-3 algebra as a generalization of QF algebras,
several extensions of this concept have been proposed for general rings. Perhaps the most …

A ring R with identity is called left QF-3'if the injective hull E (R) of the left i?-module R is
torsionless. This class of rings and the other related generalizations of quasi-Frobenius rings …

The purpose of this note is to establish a structure theorem for left QF-3 rings, an analogue to
one for QF-3 algebras by Morita [14], introducing a new notion of left QF-3 rings. It turns out …

In this paper, by a left QF-3 ring we shall always understand a ring with a (unique) minimal
faithful left module, and by a QF-3 ring we mean a ring which is both left and right QF-3 …

A left QF-3 ring R is one in which RR, the ring considered as a left module over itself, can be
embedded in a projective infective left R module Q (RR). QF-3 rings were introduced by …

In this paper, by a left QF-3 ring we shall always understand a ring with a (unique) minimal
faithful left module, and by a QF-3 ring we mean a ring which is both left and right QF-3 …

In this paper we will introduce a new class of rings which seem to deserve study. In the early
1940's Nakayama introduced and began the study of Frobenius and Quasi-Frobenius …

Let R be a ring with minimum condition on left or right ideals. It is shown that R is a QF⋅ 3
ring if and only if each finitely generated submodule of the injective hull of R, regarded as a …

A ring R (with identity) is semi-primary if it contains a nilpotent ideal N with R/N semi-simple
with minimum condition. R is called a left QF-3 ring if it contains a faithful projective injective …

In this paper the following results are proved:(i) Three classes of left QF-3 rings are closed
under taking left quotient rings respectively.(ii) A subcategory of left modules having …