Duo property for rings by the quasinilpotent perspective
Rings and Algebras
2024-05-28 v1
Abstract
In this paper, we focus on the duo ring property via quasinilpotent elements which gives a new kind of generalizations of commutativity. We call this kind of ring qnil-duo. Firstly, some properties of quasinilpotents in a ring are provided. Then the set of quasinilpotents is applied to the duo property of rings, in this perspective, we introduce and study right (resp., left) qnil-duo rings. We show that this concept is not left-right symmetric. Among others it is proved that if the Hurwitz series ring is right qnil-duo, then is right qnil-duo. Every right qnil-duo ring is abelian. A right qnil-duo exchange ring has stable range 1.
Keywords
Cite
@article{arxiv.2102.03811,
title = {Duo property for rings by the quasinilpotent perspective},
author = {Abdullah Harmanci and Yosum Kurtulmaz and Burcu Ungor},
journal= {arXiv preprint arXiv:2102.03811},
year = {2024}
}