A note on Brown-McCoy radicals of \(\Gamma\)-rings (Q1068920)

The Brown-McCoy radical, \(B(M)\) of a \(\Gamma\)-ring \(M\) was previously defined by the author. We extend Kyuno's definition of the simplicial radical \(S(M)\) to arbitrary \(\Gamma\)-rings (i.e. without any assumptions concerning unities). \(B(M)\) and \(S(M)\) are shown to be special radicals. Moreover, both are generalizations of the Brown-McCoy radical of a ring. In general, \(B(M)\neq S(M)\).