On Weak e-Reflexive Rings and Their Nil Extensions

Axioms 2026 Open access

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Authors: A A Alqahtani, Eltiyeb Ali, Khalid I. A. Ahmed
DOI: 10.3390/axioms15060396
Cited by: 1
References: 33

Abstract

In this work, we establish the relationships between weak e-reversibility and weak e-semicommutativity, introducing weak e-reflexive rings as a natural generalization of reflexive and e-reflexive rings. We demonstrate that, under specific conditions, weak e-reflexivity and weak e-reversibility coincide in Baer rings, and we provide characterizations via corner subrings and semicentral idempotents. Furthermore, we introduce e-nilpotent reflexive rings and examine their structural stability and connections within the class of generalized reflexive rings. A comprehensive analysis is provided regarding the behavior of these properties under polynomial and Dorroh extensions, as well as within matrix rings and quotient structures.

Fields of Study & Subjects

Rings Modules and Algebras Fuzzy and Soft Set Theory Advanced Algebra and Logic

Publication details

Journal / source
Axioms
Publisher
MDPI AG
Volume
15
Issue
6
Pages
396–396
Publication date
25 May 2026
Language
EN