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ON BAD SUPERNILPOTENT RADICALS

Part of: Radicals and radical properties of rings

Published online by Cambridge University Press:  15 December 2011

H. FRANCE-JACKSON
H. FRANCE-JACKSON*
Affiliation:
Department of Mathematics and Applied Mathematics, Nelson Mandela Metropolitan University, Summerstrand Campus (South), PO Box 77000, Port Elizabeth 6031, South Africa (email: cbf@easterncape.co.uk)
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Abstract

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A supernilpotent radical α is called bad if the class π(α) of all prime and α-semisimple rings consists of the one-element ring 0 only. We construct infinitely many bad supernilpotent radicals which form a generalization of Ryabukhin’s example of a supernilpotent nonspecial radical. We show that the family of all bad supernilpotent radicals is a sublattice of the lattice of all supernilpotent radicals and give examples of supernilpotent radicals that are not bad.

Keywords

supernilpotent radicalspecial radicalprime radicalBoolean ringsprime essential rings

MSC classification

Secondary: 16N80: General radicals and rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 2 , April 2012 , pp. 271 - 274
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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