In the early 1980s, Harada introduced extending and lifting properties for modules and,
simultaneously, considered two new classes of artinian rings which contain QF-rings and …

Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since
then, these classical artinian rings have continued to fascinate ring theorists with their …

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 …

This monograph is a proposed eighth and final chapter for a revised version of Rings and
Categories of Modules by Frank W. Anderson and myself (Springer-Verlag, GTM Vol. 13) …

Artinian serial principal ideal rings and artinian serial rings are tradi-tionally called
uniserialrings and generalized uniserial rings, respectively. These rings are important …

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 …

Let R be a ring. Any R-module M which is Artinian or Noetherian can be written as the direct
sum of a finite number of indecomposable R-modules. The theorem of Krull–Remak …

In this paper we assume that every ring R is an associative ring with identity and R is two-
sided artinian. The author has defined almost projective modules and almost injective …

We recall that a Quasi-Frobenius ring (QF ring), R, is a left artinian ring with unit for which the
module RR is injective. This paper has a threefold objective concerning such rings. First, we …

A RESULT ON SEMI-ARTINIAN RINGS Page 1 Proceedings of the Edinburgh Mathematical
Society (2003) 46, 63–66 c DOI:10.1017/S0013091501001067 Printed in the United …