Abstract
A quasi-Frobenius ring ( QF ring) is a left Artinian ring R with identity for which the left R-module R R is injective. Since Nakayama [8] introduced the notion of a QF ring, quasi-Frobenius rings have been extensively studied. It is well known that for any QF ring R, both R n , the ring of n × n matrices over R, and RG, group ring over R for any finite group G are both QF rings. Also any proper homomorphic image of a commutative principal ideal domain is a QF ring [3, p. 402, Exer. 2]. There are many other examples of QF rings scattered throughout the literature together with numerous characterizations of QF rings, but nowhere does there appear a systematic method for constructing QF rings in general.
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