Abstract

A radical class R of rings is elementary if it contains precisely those rings whose singly generated subrings are in R. Many examples of ele- mentary 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 dis- cussion 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.

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