Let \(R\) be a ring and \(_R\mathcal M\) the category of all left \(R\)-modules. \textit{G. Azumaya} [Nagoya Math. J. 27, 697--708 (1966; Zbl 0144.02303)] proved that if all faithful left \(R\)-modules are generators in \(_R\mathcal M\), \(R\) is left self-injective and a direct sum of indecomposable left ideals having minimal left ideals (cf. also, \textit{Y. Utumi} [ J. Algebra 6, 56--64 (1967; Zbl 0161.03803)]. However, it remains open whether \(R\) has the same structure or not if all finitely generated faithful left \(R\)-modules are generators, since the faithful left \(R\)-module (an injective cogenerator) used in his proof is not necessarily finitely generated. In this paper, it is proved that we have an affirmative answer to the above question, if \(R\) is a right perfect ring. It follows immediately that if \(R\) is a left Artinian ring, then \(R\) is quasi-Frobenius if and only if all finitely generated, faithful left \(R\)-modules are generators.