On the base radical class for associative rings
Source: Acta Mathematica Hungarica, Volume 98, Number 4, 2003 , pp. 263-272(10)
The base radical class Lb(X), generated by a class X was introduced in . It consists of those rings whose nonzero homomorphic images have nonzero accessible subrings in X. When X is homomorphically closed, Lb(X) is the lower radical class defined by X, but otherwise X may not be contained in Lb(X). We prove that for a hereditary radical class L with semisimple class S(R), Lb(S(R)) is the class of strongly R-semisimple rings if and only if R is supernilpotent or subidempotent. A number of further examples of radical classes of the form Lb(X) are discussed.
Document Type: Research Article
Affiliations: 1: Discipline of Mathematics, University of Tasmania GPO Box 252-37, Hobart, Tasmania 001, Australia E-mail: GARDNER@HILBERT.MATHS.UTAS.EDU.AU 2: School of Mathematical and Decision Sciences, Central Queensland University Rockhampton, Queensland 4702, Australia E-mail: R.MCDOUGALL@CQU.EDU.AU
Publication date: 2003-01-01