Article
Kyungpook Mathematical Journal 2024; 64(1): 1-14
Published online March 31, 2024
Copyright © Kyungpook Mathematical Journal.
A Characterization of Nonnil-Projective Modules
Hwankoo Kim∗, Najib Mahdou and El Houssaine Oubouhou
Division of Computer Engineering, Hoseo University, Asan 31499, Republic of Korea
e-mail : hkkim@hoseo.edu
Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco
e-mail : najib.mahdou@usmba.ac.ma and hossineoubouhou@gmail.com
Received: September 13, 2023; Revised: October 20, 2023; Accepted: October 23, 2023
Recently, Zhao, Wang, and Pu introduced and studied new concepts of nonnil-commutative diagrams and nonnil-projective modules. They proved that an R-module that is nonnil-isomorphic to a projective module is nonnil-projective, and they proposed the following problem: Is every nonnil-projective module nonnil-isomorphic to some projective module? In this paper, we delve into some new properties of nonnil-commutative diagrams and answer this problem in the affirmative.
Keywords: Nonnil-commutative diagram, Nonnil-exact sequence, Nonnil-projective module