On subhereditary radicals and reduced rings

Abstract

We answer some open problems on subhereditary radicals of associative rings. In particular, we show that the Brown–McCoy radical is not subhereditary and that every left or right subhereditary and left or right stable radical satisfies all these properties. The latter of these results concerns, in fact, the question whether some classes of reduced rings are closed under one-sided essential extensions. We characterize several such classes.