Abstract

Quasi-Frobenius rings (briefly, QF-'rings) form an important class of non-semisimple artinian rings. Many characterizations of QF-rings by means of small and non small idemponent in a left and right artinian ring were obtained by Harada. The purpose of the paper is to give similar characterization of a QF ring R satisfying weaker assumption. We also obtain a result of QF-quotient rings which extends Therion theorem 6.18 of [2].