Rings whose cyclics are U-modules

Ibrahim Y., Kason M. T., Truong Cong Quynh T. C. Q., Yousif M.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.21, no.01, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 01
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498822500074
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Injective, quasi-injective, quasi-continuous, U-modules, square-free and auto-invariant modules, clean and exchange rings, SUBMODULES
  • Gazi University Affiliated: Yes

Abstract

A right R-module M is called a U-module if, whenever A and B are submodules of M with A congruent to B and A boolean AND B = 0, there exist two direct summands K and T of M such that A subset of(ess) K, B subset of(ess) T and K circle plus T subset of(circle plus) M. The class of U-modules is a strict and simultaneous generalization of quasi-continuous, square-free and automorphism-invariant modules. In this paper we study the rings whose cyclics are U-modules, extending many of the known results on the subject and providing new ones.