\(\Gamma\)-rings and normal radicals (Q1915635)

Let \(M\) be a \(\Gamma\)-ring with left and right operator rings \(L\) and \(R\) respectively. For any normal radical class \(\mathcal R\) of rings it is \({\mathcal R}(L)^+={\mathcal R}(R)^*\). Let \(\mathcal R\) a supernilpotent radical class of rings. If \({\mathcal R}(L)^+={\mathcal R}(R)^*\) for every \(\Gamma\)-ring \(M\) then \(\mathcal R\) is an \(N\)-radical.