A construction of supernilpotent radical classes

Abstract

AbstractIn a recent paper van Leeuwen and Heyman constructed a supernilpotent radical class using the class of almost nilpotent rings. Using a similar construction, for any class C satisfying the following four properties we obtain a superrnlpotent radical class containing C.(N1) C contains the class Z of all zero rings.(N2) C is hereditary.(N3) C is homomorphically closed.(N4) If A and A/I are elements of C for some ideal I of a ring A, then A ∈ C.Every supernilpotent radical class P clearly satisfies these conditions. For any such radical class we define the class of almost radical rings and use these to construct a new radical class P2 which contains the given one. Also, we give a characterization for dual supernilpotent radicals.