QF-1 Rings

Abstract

<p> A ring R is said to be QF-1 if every finitely generated faithful R-module has the double centralizer property (or is balanced). A necessary and sufficient condition for an artinian ring to be QF-1 is given. The class of QF-1 rings properly contains the class of QF rings and this is shown by an example. Several constructions of modules which are not balanced are collected. Finally, the structure of artinian local QF-1 rings which are finitely generated over their centers is gotten. This is a generalization of theorems of Floyd, and, Fuller and Dickson.</p>