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Further remarks on elementary radicals and associated filters of ideals

Cojuhari, EP and Gardner, BJ 2020 , 'Further remarks on elementary radicals and associated filters of ideals' , Bulletin of the Australian Mathematical Society, vol. 103, no. 3 , pp. 450-460 , doi: 10.1017/S0004972720001021.

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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.

Item Type: Article
Authors/Creators:Cojuhari, EP and Gardner, BJ
Keywords: radical class, radical filter
Journal or Publication Title: Bulletin of the Australian Mathematical Society
Publisher: Australian Mathematics Publ Assoc Inc
ISSN: 0004-9727
DOI / ID Number: 10.1017/S0004972720001021
Copyright Information:

© 2020 Australian Mathematical Publishing Association Inc

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