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arXiv · 2102.03811

Duo property for rings by the quasinilpotent perspective

Abdullah Harmanci·Yosum Kurtulmaz·Burcu Ungor
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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 $H(R; \alpha)$ 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.

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Abdullah Harmanci, Yosum Kurtulmaz, Burcu Ungor. 2021-02-07. Duo property for rings by the quasinilpotent perspective. https://doi.org/10.15330/cmp.13.2.485-500

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