In this article we consider only associative rings with nonzero identity and unitary modules. A
ring R is called a two-sided PF-ring or a ring with perfect duality if it is a left and right PF-ring …

1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …

There are many results of a homological nature which may be generalized from Noetherian
rings to coherent rings. In this process, finitely generated modules should in general be …

It is well known that if R is a ring such that each right R-module Ž. embeds in a free module,
then R is a quasi-Frobenius QF ring. However, if the embedding is restricted to finitely …

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 quasi-Frobenius ring (QF ring) is a left Artinian ring R with identity for which the left R-
module RR is injective. Since Nakayama [8] introduced the notion of a QF ring, quasi …

The purpose of this note is to give a characterization of QF-3 rings and apply this result to
obtain a characterization of PF rings.(See below ibr definitions.) Throughout this note let R …

Let Rbe a commutative Artin ring with identity e, and let Μ be a left Λ-module. For any
subsets/CR, Ν C Μwe put An^/)={ae Μ:/a= 0}, AnR (N)={re R: rN= 0}. The moduleRQ is …

The idea of writing this book came roughly at the time of publication of my graduate text
Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching …

Tachikawa showed that a left perfect ring R is an injective cogenerator in the category of all
right R-modules iff there holds:(right FPF) every finitely generated faithful right module …