Duo property for rings by the quasinilpotent perspective
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 H(R; α) 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.
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