a1 Department of Mathematics Institute of Advanced Studies, Australian National University, Canberra, ACT.
Dickson's construction  of radical and semi-simple classes for certain abelian categories is a rather straightforward procedure in comparison with the methods traditionally used in more general situations. In §2 of the present paper we use a well-known characterization of the lower radical class to obtain, via consideration of maps with accessible images, a similar “homomorphic orthogonality” characterization of radical and semi-simple classes of associative rings. By substituting certain other subring properties for accessibility, we are then able to obtain simple constructions of various types of radical classes, including those which are strict in the sense first used by Kurosh  for groups.
(Received March 13 1973)