Characterizations of the Brown-McCoy radical
type: Item
instance of: scholarly article
title: Characterizations of the Brown-McCoy radical
zbMATH Open document ID: 0588.17003
DOI: 10.1007/BF01961014
author: B. de la Rosa
author: R. Wiegandt
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: Let \({\mathcal A}\) be a universal class of rings or near rings (not necessarily associative). The authors show that the Brown-McCoy radical class \({\mathcal G}\) in \({\mathcal A}\) coincides with the uniquely determined largest homomorphically closed class of rings (near rings) in \({\mathcal A}\) without unity. Besides this characterization as a lower radical they present also a characterization of \({\mathcal G}\) as an upper radical in a universal class \({\mathcal A}\) of alternative or near rings. In fact, \({\mathcal G}\) is the upper radical determined by the uniquely determined largest hereditary class of rings (near rings) in \({\mathcal A}\) with unity. With respect to this upper class representation, \({\mathcal G}\) has the intersection property. For associative rings A, it is shown that \(r_ 3(A)=A\) in A-mod if and only if \({\mathcal G}(A)=A\) in the category of rings, where \(r_ 3\) is a module-radical, introduced by the first author [Publ. Math. 27, 7-12 (1980; Zbl 0456.16009)].
Mathematics Subject Classification ID: 17A65
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16Y30
zbMATH DE Number: 3944088
zbMATH Keywords: alternative rings
zbMATH Keywords: universal class of rings
zbMATH Keywords: near rings
zbMATH Keywords: Brown-McCoy radical class
zbMATH Keywords: lower radical
zbMATH Keywords: upper radical
zbMATH Keywords: intersection property
zbMATH Keywords: associative rings
zbMATH Keywords: module-radical
MaRDI profile type: Publication
cites work: Radicals and subdirect decomposition
cites work: Q3904722
cites work: On the Andrunakievich lemma for alternative rings
cites work: Q3904723
cites work: Q5651337
full work available at URL: https://doi.org/10.1007/bf01961014
OpenAlex ID: W2023262908
description: scientific article; zbMATH DE number 3944088