Rings whose cyclics are DU-modules
Yasser Ibrahim , Tamer Koşan & Mohamed Yousif
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt and,
Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia;
Department of Mathematics, Gazi University, Ankara, Turkey;
Department of Mathematics, The Ohio State University, Lima, Ohio 45804, USA.
Pages 86-97 | Received 10 June 2021, Accepted 03 August 2021, Published 01 June 2022
Abstract
A right R-module M is called a D 4-Module if for any two direct summands A and B of M with M =A +B and M/A \cong M/B, we have A \cap B \subseteq ^{ \oplus }M. The module M is called a Dual-Utumi-Module (D U-module) if M is a D 4-module and for any two proper submodules A and B of M with M/A \cong M/B and A +B =M, both A and B lie over direct summands of M. The notion of D U-modules is a simultaneous and strict generalization of both the quasi-discrete as well as the dual-square-free modules. In this paper,we study the modules whose factors are D U-modules (D 4-modules), extending some of the known results on quasi-discrete modules and obtaining new ones.
Keywords: Projective, quasi-projective, quasi-discrete, Utumi, Dual-Utumi and dual-square-free modules.
MSC numbers: Primary 16D40, 16D50, 16D60; Secondary 16L30, 16L60, 16P20, 16P40, 16P60.
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