Density relative to a torsion theory

If $(\Im, \mathcal{F})$ is a torsion theory on Mod $R$, then a ring $B$ of biendomorphisms of a $\Im$-cocritical module is topologized. Moreover, if a certain factor module of $R$ is quasi-projective, a ring monomorphism $\varphi :R \to B$ is found such that $\varphi (R)$ is topologically dense in $B$. This is done in such a way that when $(\Im, \mathcal{F})$ is the torsion theory in which every module is torsion free, the Jacobson density theorem is recovered.