REGULARITIES AND COMPLEMENTARY RADICALS

Abstract

In this paper we consider a class of Hoehnke radicals of associative rings. A radical H from this class is constructed using generalized semi-prime ideals determined by a ring regularity. It is shown that different regularitiesMaybe used to construct the same radical H. Furthermore, we show that the K.A.-radical corresponding to one of the regularities which determines H is in fact complementary to H. As special cases we have that the radical defined by f-regularity is complementary to Bear's lower radical β, the radical defined by C-regularity is complementary to the generalized nil-radical N_g and that the quasi-radical and the λ-radical are complementary.