Upper radicals and essential ideals

Dwight M. Olson; Terry L. Jenkins

doi:10.1017/S1446788700017870

Upper radicals and essential ideals

Published online by Cambridge University Press: 09 April 2009

Dwight M. Olson and

Terry L. Jenkins

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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 .