Near-ring radicals depending only on the additive groups (Q1281272)

Let \(\mathbf U\) be a universal class of (right) near-rings. Hoehnke radicals in \(\mathbf U\) which are independent of the multiplication operation are considered. Three types of multiplicative independence are possible for a Hoehnke radical \(\rho\): (i) The underlying sets \(\rho(N,+,\bullet)\) and \(\rho(N,+,*)\) coincide; (ii) \((N,+,\bullet)\in{\mathbf S}\) if and only if \((N,+,*)\in{\mathbf S}\); (iii) \(\rho(N,+,\bullet)\in{\mathbf R}\) if and only if \((N,+,*)\in{\mathbf R}\), where \(\mathbf R\) and \(\mathbf S\) denote the radical and semisimple classes of \(\rho\), respectively. Various results are proved concerning the relationships between these three conditions when certain conditions are imposed on \(\mathbf U\). (Also submitted to MR).