On the construction of quasi-Frobenius rings

AbstractA 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-Frobenius rings have been extensively studied. It is well known that for any QF ring R, both Rn, 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