This paper consists of three parts. The first is devoted to investigating the equivalence and
left-right symmetry of several conditions known to characterize finite dimensional algebras …

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 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 …

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 …

Mochizuki has considered a hereditary QF-3 algebra in [6]. In this note we shall study a PP-
ring with minimal condition or of semi-primary. To this purpose we generalize a notion of QF …

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 …

The notion of QF-3 algebras was introduced first by Thrall [15J as a generalization of quasi-
Frobenius algebras and later extended to the notion of QF-3 rings (cf.[5, 4, 16, 12]). Here we …

Introduction and Preliminaries. Nakayama [9] suggested that algebras be classified
according to the length of a right projective, injective resolution of the algebra as a left …

The class of quasi-Frobenius rings (short: QF rings) is one of the most interesting classes of
non-semisimple rings. Since RM Thrall [53] introduced QF-1, QF-2 and QF-3 rings as its …

Let R be a ring with identity. R is left QF-3 if R has a minimal faithful (left) module, ie, a
faithful (left) module, which is (isomorphic to) a summand of every faithful (left) module. We …