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ON BASE RADICAL OPERATORS FOR CLASSES OF FINITE ASSOCIATIVE RINGS

Part of: Radicals and radical properties of rings

Published online by Cambridge University Press:  18 July 2018

R. G. MCDOUGALL Open the ORCID record for R. G. MCDOUGALL [Opens in a new window]  and
L. K. THORNTON Open the ORCID record for L. K. THORNTON [Opens in a new window]
R. G. MCDOUGALL
Affiliation:
Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Maroochydore, Queensland 4588, Australia email rmcdouga@usc.edu.au
L. K. THORNTON*
Affiliation:
Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Maroochydore, Queensland 4588, Australia email lauren.thornton@research.usc.edu.au
*
✉lauren.thornton@research.usc.edu.au
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Abstract

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In this paper, class operators are used to give a complete listing of distinct base radical and semisimple classes for universal classes of finite associative rings. General relations between operators reveal that the maximum order of the semigroup formed is 46. In this setting, the homomorphically closed semisimple classes are precisely the hereditary radical classes and hence radical–semisimple classes, and the largest homomorphically closed subclass of a semisimple class is a radical–semisimple class.

Keywords

base radicalbase semisimplefinite associative ring

MSC classification

Primary: 16N80: General radicals and rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 239 - 250
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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