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FURTHER REMARKS ON ELEMENTARY RADICALS AND ASSOCIATED FILTERS OF IDEALS

Part of: Structure and classification of infinite or finite groups Radicals and radical properties of rings

Published online by Cambridge University Press:  08 October 2020

E. P. COJUHARI Open the ORCID record for E. P. COJUHARI [Opens in a new window]  and
B. J. GARDNER Open the ORCID record for B. J. GARDNER [Opens in a new window]
E. P. COJUHARI
Affiliation:
Department of Mathematics, Technical University of Moldova, Ştefan cel Mare av. 168, MD 2004 Chişinău, Moldova e-mail: elena.cojuhari@mate.utm.md
B. J. GARDNER*
Affiliation:
Discipline of Mathematics, University of Tasmania PB37, Hobart, Tasmania7001, Australia
*
e-mail: Barry.Gardner@utas.edu.au
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Abstract

Ryabukhin showed that there is a correspondence between elementary radical classes of rings and certain filters of ideals of the free ring on one generator, analogous to the Gabriel correspondence between torsion classes of left unital modules and certain filters of left ideals of the coefficient ring. This correspondence is further explored here. All possibilities for the intersection of the ideals in a filter are catalogued, and the connections between filters and other ways of describing elementary radical classes are investigated. Some generalisations to nonassociative rings and groups are also presented.

Keywords

elementary radical classradical filtertorsion class

MSC classification

Primary: 16N80: General radicals and rings
Secondary: 20E99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 450 - 460
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

In memory of Yuri Ryabukhin

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