Characterizations of \(QF\)-rings in terms of pseudo
\(C^*\)-injectivity

Abstract. As a generalization of quasi-injective modules, an \(R\)-module \(M\) is pseud
\(N\)-\(c^*\)-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 \(R^{(\mathbb{N})}_R\) is injective then \(R\) is quasi Frobenius.