*-q-central idempotent and *-quasi-normal ring
Year: 2025
Type: article
Abstract: In a *-ring, an idempotent e ? R is called *-quarter-central (or *-q-central for short) if e*R(1-e)Re* = 0. If all idempotents in a *-ring R are *-q-central, R is said to be a *-quasi-normal ring. In the paper, we prove that in a *-ring, each *-q-central idempotent must be q-central, and the converse of the conclusion is not true. Moreover, we give some equivalent conditions to claim when a q-central idempotent is *-q-central. From the viewpoint of currently prevailing generalizations of rings in the literature, *-q-central idempotents and *-quasi-normal rings are the generalizations of q-central idempotents and quasi-normal rings, respectively.
Source: Filomat
DOI: 10.2298/fil2505573c
Authors: Liufeng Cao, Junchao Wei
Institutions: Yancheng Institute of Technology, Yangzhou University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412757615