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On the radical theory of Andrunakievich varieties

Published online by Cambridge University Press:  17 April 2009

P.N. Ánh ,
N.V. Loi  and
R. Wiegandt
P.N. Ánh
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest, PO Box 127, H-1364, Hungary.
N.V. Loi
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest, PO Box 127, H-1364, Hungary.
R. Wiegandt
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest, PO Box 127, H-1364, Hungary.
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Abstract

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In 1978 Anderson and Gardner investigated semisimple classes and recently Buys and Gerber developed the theory of special radicals in Andrunakievich varieties. In this note we continue the study of radical theory in Andrunakievich varieties. Sharpening some of the results of Anderson and Gardner we prove versions of Sands' Theorem characterizing semisimple classes by regularity, coinductivity and being closed under extensions. In the proof we follow a new method which avoids calculations with defining identities of the variety. We generalize van Leeuwen's Theorem characterizing semisimple classes of hereditary radicals as classes being regular and closed under essential extensions and subdirect sums.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 2 , April 1985 , pp. 257 - 269
Copyright
Copyright © Australian Mathematical Society 1985

References

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