In ring theory, duoness and Zhou radical which is known as delta ideal have important roles. this paper, we consider both concepts together by studying on radical. By means of study, obtain a new kind generalizations commutativity. Firstly, determine some rings, then applied to the duo property so introduce notion right (left) dZr rings. We show that not left-right symmetric. investigate relati...

We show that there exist noncommutative Ore extensions in which every right ideal is two-sided. This answers a problem posed by Marks in [5]. We also provide an easy construction of one sided duo rings.

In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitabl...