The relationship between the radical of a ring R and a structural matr
ix ring over R has been determined for some radicals. We continue thes
e investigations, amongst others, determining exactly which radicals g
amma have the property (rho,R))=M(rho(s),gamma(R))++M(rho(a),gamma(+)(
R)) for any structural matrix ring M(rho,R) and finding beta(M(rho,R))
for any hereditary subidempotent radical beta.