A note on Mal'tsev-Neumann products of radical classes

A radical class �� of rings is <i>elementary</i> if it contains precisely those rings whose singly generated subrings are in ��. Many examples of elementary radical classes are presented, and all those which are either contained in the Jacobson radical class or disjoint from it are described. There is a discussion of Mal'tsev products of radical classes in general, in which it is shown, among other things, that a product of elementary radical classes need not be a radical class, and if it is, it need not be elementary.