Reversibility of rings with respect to the Zhou Radical

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.