Duo property for rings by the quasinilpotent perspective

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Harmanci A., Kurtulmaz Y., Ungor B.

CARPATHIAN MATHEMATICAL PUBLICATIONS, vol.13, no.2, pp.485-500, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.15330/cmp.13.2.485-500
  • Journal Name: CARPATHIAN MATHEMATICAL PUBLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.485-500
  • Keywords: quasinilpotent element, duo ring, qnil-duo ring
  • Hacettepe University Affiliated: Yes

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.