Duo property for rings by the quasinilpotent perspective

  • A. Harmanci Department of Mathematics, Hacettepe University, Ankara, Turkey
  • Y. Kurtulmaz Department of Mathematics, Bilkent University, Ankara, Turkey https://orcid.org/0000-0001-6089-4366
  • B. Ungor Department of Mathematics, Ankara University, Ankara, Turkey
Keywords: quasinilpotent element, duo ring, qnil-duo ring
Published online: 2021-10-17

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 rings 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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How to Cite
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HarmanciA.; KurtulmazY.; UngorB. Duo Property for Rings by the Quasinilpotent Perspective. Carpathian Math. Publ. 2021, 13, 485-500.