Reversible ring property via idempotent elements
Abstract
Regarding the question of how idempotent elements affect reversible property of rings, we study a version of reversibility depending on idempotents. In this perspective, we introduce {\it right} (resp., {\it left}) {\it -reversible rings}. We show that this concept is not left-right symmetric. Basic properties of right -reversibility in a ring are provided. Among others it is proved that if is a semiprime ring, then is right -reversible if and only if it is right -reduced if and only if it is -symmetric if and only if it is right -semicommutative. Also, for a right -reversible ring , is a prime ring if and only if it is a domain. It is shown that the class of right -reversible rings is strictly between that of -symmetric rings and right -semicommutative rings.
Cite
@article{arxiv.2011.10843,
title = {Reversible ring property via idempotent elements},
author = {Handan Kose and Burcu Ungor and Abdullah Harmanci},
journal= {arXiv preprint arXiv:2011.10843},
year = {2020}
}