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A supernilpotent non-special radical class

Published online by Cambridge University Press:  17 April 2009

L.C.A. van Leeuwen  and
T.L. Jenkins
L.C.A. van Leeuwen
Affiliation:
Mathematisch Instituut, Rijksuniversiteit te Groningen, Groningen, Netherlands;
T.L. Jenkins
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming, USA.
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Abstract

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Let F be the upper radical determined by all fields. The supernilpotent radical classes which are not special have thus far always contained F properly. The purpose of this note is to construct a countably infinite number of supernilpotent radical classes which are not special and each of which is properly contained in F. The construction involves a ring due to Leavitt which is interesting in its own right and is not generally known. All rings considered are associative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 343 - 348
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Divinsky, Nathan, Rings and radicals (University of Toronto Press, Toronto, 1965).Google Scholar
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[3]Snider, Robert L., “Lattices of radicals”, Pacific J. Math. 40 (1972), 207–220.CrossRefGoogle Scholar