<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Radical Classes Closed Under Products

University of Tasmania Private Bag 37 Hobart, Tas. 7001, Australia

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Radical Classes Closed Under Products"}

This is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups,...

Radical Classes Closed Under Products

Published Online: Mar 05, 2014

Page range: 103 - 132

DOI: https://doi.org/10.2478/auom-2013-0047

Keywords
Radical class, product, slender, ring, group, module

This content is open access.

Radical Classes Closed Under Products

Published Online: Mar 05, 2014

Page range: 103 - 132

DOI: https://doi.org/10.2478/auom-2013-0047

KeywordsRadical class, product, slender, ring, group, module

This content is open access.

Keywords
Radical class, product, slender, ring, group, module