On the radicals of structural matrix rings

The relationship between the radical of a ring R and a structural matrix ring over R has been determined for some radicals. We continue these investigations, amongst others, determining exactly which radicals γ have the property γ(M(ρ, R)) = M(ρ_s, γ(R)) + + M(ρ_a,γ^-(R)) for any structural matrix ring M(ρ, R) and finding β(M(ρ, R)) for any hereditary subidempotent radical β.