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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 Type:	Refereed Article
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
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
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