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On Dual Radicals and Ring Elements

Published online by Cambridge University Press:  09 April 2009

B. De La Rosa  and
R. Wiegandt
B. De La Rosa
Affiliation:
Department of MathematicsUniversity of the OrangeFree State Bloemfontein 9300 South, Africa
R. Wiegandt
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences Budapest, V. Re´ltanoda u. 13–15, Hungary
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Abstract

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If a property P of ring elements satisfies conditions (a)-(d), then the largest homomorphically closed class having no non-zero P-element is a dual radical in the sense of Andrunakievič, and every dual radical can be obtained in this way. Also properties defined by polynomials are considered and as an application we get various characterizations of the Behrens radical.

Keywords

subdirectly irreducible ringradical classupper radicalspecial radicaldual radicalBehrens radical
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 164 - 170
Copyright
Copyright © Australian Mathematical Society 1988

References

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