Rings which are duo on Zhou radical
Date
2022-09-02Source Title
São Paulo Journal of Mathematical Sciences
Print ISSN
1982-6907
Electronic ISSN
2316-9028
Publisher
Springer
Volume
16
Issue
2
Pages
871 - 892
Language
English
Type
ArticleItem Usage Stats
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Abstract
In ring theory, duoness and Zhou radical which is known as delta ideal have important roles. In this paper, we consider both concepts together by studying duoness on Zhou radical. By means of this study, we obtain a new kind of generalizations of commutativity. Firstly, we determine Zhou radical of some rings, then Zhou radical is applied to the duo property of rings, so we introduce a notion of right (left) dZr rings. We show that this notion is not left-right symmetric. We investigate some relations between right dZr rings and certain rings, and also deal with some ring extensions in terms of dZr property.