Duo property for rings by the quasinilpotent perspective

Abstract

In this paper, we focus on the duo ring property via quasinilpotent elements, which gives anew kind of generalizations of commutativity. We call this kind of ringsqnil-duo. Firstly, someproperties of quasinilpotents in a ring are provided. Then the set of quasinilpotents is applied tothe duo property of rings, in this perspective, we introduceand study right (resp., left) qnil-duorings. We show that this concept is not left-right symmetric. Among others, it is proved that if theHurwitz series ringH(R;α)is right qnil-duo, thenRis right qnil-duo. Every right qnil-duo ring isabelian. A right qnil-duo exchange ring has stable range 1.