Duo property for rings by the quasinilpotent perspective
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 pro...
| Main Authors: | , , |
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| Format: | Article |
| Sprog: | English |
| Udgivet: |
Vasyl Stefanyk Precarpathian National University
2021-10-01
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| Serier: | Karpatsʹkì Matematičnì Publìkacìï |
| Fag: | |
| Online adgang: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4761 |
| Summary: | 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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| ISSN: | 2075-9827 2313-0210 |