TY - JOUR
AU - Harmanci, A.
AU - Kurtulmaz, Y.
AU - Ungor, B.
PY - 2021/10/17
Y2 - 2024/04/24
TI - Duo property for rings by the quasinilpotent perspective
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 13
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.13.2.485-500
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/4761
SP - 485-500
AB - <p>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 rings <em>qnil-duo</em>. 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 $H(R; \alpha)$ is right qnil-duo, then $R$ is right qnil-duo. Every right qnil-duo ring is abelian. A right qnil-duo exchange ring has stable range 1.</p>
ER -