Quasi-frobenius (= QF) rings have many interesting characterizations. One such, due to
Ikeda [17] is that these rings are right (left) artinian and right (left) self-injective. Thus, if R is …

This note discusses the structure of a ring R with the ascending chain condition (= acc) on
annihilator left ideals having the property that each module homomorphism from a principal …

Let R be a ring with identity 1. We denote the category of unital right (respectively left) R-
modules by 'U&m). MR will signify ME YJl&M E $ tJl). We will be concerned with certain …

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 …

1) R satisfifies (\#) . Page 1 Hokkaido Mathematical Journal Vol. 13 (1984) p. Lifting modules,
extending modules and their applications to QF-rings By Kiyoichi OSHIRO (Received June 21 …

Theorem (K6the-Cohen-Kaplansky). A commutative ring R has the property that each of its R-
modules is a direct sum of cyclic modules if and only if R is an artinian principal ideal ring …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …

In this paper we are mainly concerned with rings satisfying the descending chain condition
(dcc) on left principal ideals. Such rings are called left coperfect rings in this paper. When 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 …

Introduction. Let A be a finite-dimensional algebra with identity element over a field O. Let M
be a finitely generated left A-module. Then M, when regarded as a left representation space …