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Essential ideals, homomorphically closed classes and their radicals

Published online by Cambridge University Press:  09 April 2009

T. L. Jenkins  and
H. J. le Roux
T. L. Jenkins
Affiliation:
The University of WyomingLaramie, Wyoming 82071, U.S.A.
H. J. le Roux
Affiliation:
University of the Orange Free StateBloemfontein 9300, Republic of South Africa
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Abstract

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Olson and Jenkins defined E(M) to be the class of all rings each nonzero homomorphic image of which contains either a nonzero M-ideal or an essential ideal where M, is any class of rings. E(M) was proven to be a radical class and various classes M were considered. Here the class E(M) is partitioned into two classes: H the class of all rings each nonzero homomorphic image of which has a proper essential ideal and the class H(M) of all rings each nonzero homomorphic image of which contains an M-ideal. It is shown that H is a radical class and under certain conditions H(M) is also a radical class. Various properties placed on M yield several well-known radical classes and an infinite number of supernilpotent nonspecial radical classes is constructed.

Keywords

upper radicalessential ideal.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 3 , December 1982 , pp. 356 - 363
Copyright
Copyright © Australian Mathematical Society 1982

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