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Essentially closed radical classes

Published online by Cambridge University Press:  09 April 2009

N. V. Loi
N. V. Loi
Affiliation:
L Eötvös UniversityBudapestHungary
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Abstract

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The main goal of this paper is to describe radical classes closed under essential extensions. It turns out that such classes are precisely the homomorphically closed semisimple classes, and hence a radical class is essentially closed if and only if it is subdirectly closed. Moreover, a class is closed under homomorphic images, direct sums and essential extensions if and only if it is an essentially closed radical class. Also radical classes are investigated which are closed under Dorroh essentially extensions only, such a radical class R consists of idempotent rings provided that R does not contain the ring of integers, meanwhile all the other radicals satisfy this requirement. A description of (hereditary and) Dorroh essentially closed radicals is given in Theorem 4.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 1 , August 1983 , pp. 132 - 142
Copyright
Copyright © Australian Mathematical Society 1983

References

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