Rings over which some preradicals are torsions

Let $R$ be an associative ring with identity and $z$ be a pretorsion such that its filter consists of the essential left ideals of the ring $R$. In this paper, it is proved that every preradical $r\ge z$ of $R-Mod$ is a torsion if and only if the ring $R$ is a finite direct sum of pseudoinjective simple rings.