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Radical classes closed under products
Citation
Gardner, BJ, Radical classes closed under products, Analele Stiintifice ale Universitatii Ovidius Constanta, 21, (3) pp. 103-132. ISSN 1224-1784 (2013) [Refereed Article]
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Copyright Statement
Copyright 2013 Tipografia Universitatii Ovidius
Official URL: http://www.anstuocmath.ro/volume-xxi-2013-fascicol...
DOI: doi:10.2478/auom-2013-0047
Abstract
This is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups, abelian ℓ-groups and modules are treated. We have attempted to account for all published results relevant to this topic. Many or most of these were not, as published, expressed in radical theoretic terms, but have consequences for radical theory which we point out. A fruitful source of results and examples is the notion of slenderness for abelian groups together with its several variants for other structures. We also present a few new results, including examples and a demonstration that e-varieties of regular rings are product closed radical classes of associative rings.
Item Details
Item Type: | Refereed Article |
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Keywords: | radical class, product, slender, ring, group, module |
Research Division: | Mathematical Sciences |
Research Group: | Pure mathematics |
Research Field: | Group theory and generalisations |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | Gardner, BJ (Dr Barry Gardner) |
ID Code: | 89200 |
Year Published: | 2013 |
Deposited By: | Mathematics and Physics |
Deposited On: | 2014-02-26 |
Last Modified: | 2014-08-08 |
Downloads: | 0 |
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