Reversibility of rings with respect to the Zhou Radical

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.