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Upper radicals and essential ideals

Published online by Cambridge University Press:  09 April 2009

Dwight M. Olson  and
Terry L. Jenkins
Dwight M. Olson
Affiliation:
Cameron University, Lawton, OK 73505, USA
Terry L. Jenkins
Affiliation:
University of Wyoming, Laramie, Wyoming 82071, USA
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Abstract

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For any class of rings it is shown that the class (M) of all rings each nonzero homomorphic image of which contains either a nonzero -ideal or an essential ideal is a radical class. If is a class of simple rings the upper radical generated by , (M), is shown to be equal to (M) where ' is the class of simple rings complementary to .

Keywords

upper radicalessential ideal
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 4 , April 1981 , pp. 385 - 389
Copyright
Copyright © Australian Mathematical Society 1981

References

Armendariz, E. P. (1968), ‘Direct and subdirect sums of simple rings with unit’, Amer. Math. Monthly 75, 746–748.CrossRefGoogle Scholar
Divinsky, N. (1965), Rings and radicals (University of Toronto Press).Google Scholar