Duo property for rings by the quasinilpotent perspective

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Harmanci A., Kurtulmaz Y., ÜNGÖR B.

Carpathian Mathematical Publications, cilt.13, sa.2, ss.485-500, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15330/cmp.13.2.485-500
  • Dergi Adı: Carpathian Mathematical Publications
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.485-500
  • Anahtar Kelimeler: quasinilpotent element, duo ring, qnil-duo ring
  • Ankara Üniversitesi Adresli: Evet

Özet

© Harmanci A., Kurtulmaz Y., Ungor B., 2021.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; 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.