On CNZ ring property via idempotent elements
Abstract
In this paper, the concept of e−CNZ rings is introduced as a generalization of symmetric rings and a particular case of e−reversible rings. Regarding the question of how idempotent elements affect CNZ property of rings. In this note, we show that e−CNZ is not left-right symmetric. We present examples of right e−CNZ rings that are not CNZ and basic properties of right e − CNZ are provided. Some subrings of matrix rings and some extensions of rings such as Jordan extension are investigated in terms of right e−CNZ.
Copyright © 2022 Iman Jalal Ali, Chenar Abdul Kareem Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
I. J. Ali, C. A. K. Ahmed, On CNZ ring property via idempotent elements, J. Math. Comput. Sci. 12 (2022), 146. https://doi.org/10.28919/jmcs/7356
BibTeX
@article{Ali2022,
author = {Ali, Iman Jalal and Ahmed, Chenar Abdul Kareem},
title = {On CNZ ring property via idempotent elements},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {146},
doi = {10.28919/jmcs/7356}
}