Reversibility of rings with respect to the Zhou Radical

TL;DR

This paper investigates the properties and extensions of rings that are $ ext{ extdelta}$-reversible, meaning zero products imply their reverses are in the Zhou radical, contributing to the understanding of ring structure related to the Zhou radical.

Contribution

It introduces the concept of $ ext{ extdelta}$-reversible rings and explores their properties and extensions, advancing the theoretical understanding of ring reversibility related to the Zhou radical.

Findings

Characterization of $ ext{ extdelta}$-reversible rings

Properties of $ ext{ extdelta}$-reversible rings

Extensions of $ ext{ extdelta}$-reversible rings

Abstract

Let $R$ be a ring with identity and $\delta(R)$ denote the Zhou radical of $R$. A ring $R$ is called {\it $\delta$-reversible} if for any $a$, $b \in R$, $ab = 0$ implies $ba \in \delta(R)$. In this paper, we give some properties of $\delta$-reversible rings. We examine some extensions of $\delta$-reversible rings.