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Essential covers and complements of radicals

Published online by Cambridge University Press:  17 April 2009

Gary F. Birkenmeier  and
Richard Wiegandt
Gary F. Birkenmeier
Affiliation:
Department of MathematicsUniversity of Southwestern LouisianaLafayette LA 70504–1010United States of America e-mail: gfb1127@usl.edu
Richard Wiegandt
Affiliation:
Mathematical InstituteHungarian Academy of SciencesPO Box 127H-1364 BudapestHungary e-mail: wiegandt@math-inst.hu
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Abstract

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We show that a radical has a semisimple essential cover if and only if it is hereditary and has a complement in the lattice of hereditary radicals. In 1971 Snider gave a full description of supernilpotent radicals which have a complement. Recently Beidar, Fong, Ke, and Shum have determined radicals with semisimple essential covers. Using their results, we are able to provide a lower radical representation of complemented subidempotent radicals. This completes Snider's description of hereditary complemented radicals.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 261 - 266
Copyright
Copyright © Australian Mathematical Society 1996

References

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