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On the Base Radical Class for Associative Rings

Citation

Gardner, BJ and McDougall, RG, On the Base Radical Class for Associative Rings, Acta Mathematica Hungarica, 98, (4) pp. 263-272. ISSN 0236-5294 (2003) [Refereed Article]

DOI: doi:10.1023/A:1022882010815

Abstract

The base radical class ℒb(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, 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 R 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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Algebra and Number Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Gardner, BJ (Dr Barry Gardner)
ID Code:25432
Year Published:2003
Deposited By:Mathematics
Deposited On:2003-08-01
Last Modified:2004-04-20
Downloads:0

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