A characterization of nonnil-projective modules (Q6557975)

Recently, \textit{W. Zhao} et al. [Commun. Algebra 50, No. 7, 2854--2867 (2022; Zbl 1487.13020)] introduced and studied new concepts of nonnilcommutative diagrams and nonnil-projective modules. They proved that an \(R\)-module that is nonnil-isomorphic to a projective module is nonnil-projective. Further they posed the following problem: Is every nonnil-projective module nonnil-isomorphic to some projective module? In this paper, author obtained some new properties of nonnil-commutative diagrams and answer this problem in the affirmative.