CHARACTERIZATIONS OF QF-RINGS IN TERMS OF PSEUDO C∗-INJECTIVITY

As a generalization of quasi-injective modules, an R-module M is pseudo N -c∗-injective for every R-module N iff M is injective. In view of this new fact, we can get new generalizations of the following important observations taking the pseudo N -c∗-injectivity instead of the continuity and the injectivity, respectively: if R is right continuous, left min-CS and satisfies ACC on its right annihilators then R is quasi Frobenius, and if R (N) R is injective then R is quasi Frobenius.