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On subhereditary radicals and reduced rings

Published online by Cambridge University Press:  12 July 2007

K. I. Beidar ,
W.-F. Ke  and
E. R. Puczyłowski
K. I. Beidar
Affiliation:
Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan
W.-F. Ke
Affiliation:
Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Banacha 2, Poland
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Abstract

We answer some open problems on subhereditary radicals of associative rings. In particular, we show that the Brown–McCoy radical is not subhereditary and that every left or right subhereditary and left or right stable radical satisfies all these properties. The latter of these results concerns, in fact, the question whether some classes of reduced rings are closed under one-sided essential extensions. We characterize several such classes.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 2 , April 2002 , pp. 255 - 266
Copyright
Copyright © Royal Society of Edinburgh 2002

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