On the base radical class for associative rings

Authors: Gardner B.J.¹; McDougall R.G.²

Source: Acta Mathematica Hungarica, Volume 98, Number 4, 2003 , pp. 263-272(10)

Publisher: Springer

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Abstract:

The base radical class L_b(X), generated by a class X was introduced in [12]. It consists of those rings whose nonzero homomorphic images have nonzero accessible subrings in X. When X is homomorphically closed, L_b(X) is the lower radical class defined by X, but otherwise X may not be contained in L_b(X). We prove that for a hereditary radical class L with semisimple class S(R), L_b(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 L_b(X) are discussed.

Keywords: associative rings; base radical class

Language: English

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