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A construction of supernilpotent radical classes

Published online by Cambridge University Press:  09 April 2009

Dwight M. Olson
Dwight M. Olson
Affiliation:
Department of Mathematics Cameron UniversityLawton, Oklahoma 73505, U.S.A.
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Abstract

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In a recent paper van Leeuwen and Heyman constructed a supernilpotent radical class using the class of almost nilpotent rings. Using a similar construction, for any class C satisfying the following four properties we obtain a superrnlpotent radical class containing C.

(N1) C contains the class Z of all zero rings.

(N2) C is hereditary.

(N3) C is homomorphically closed.

(N4) If A and A/I are elements of C for some ideal I of a ring A, then A ∈ C.

Every supernilpotent radical class P clearly satisfies these conditions. For any such radical class we define the class of almost radical rings and use these to construct a new radical class P2 which contains the given one. Also, we give a characterization for dual supernilpotent radicals.

Keywords

almost nilpotentsupernilpotentweakly specialdual radicals.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 86 - 91
Copyright
Copyright © Australian Mathematical Society 1982

References

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