Rings which are duo on Zhou radical

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.