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Radicals and polynomial rings

Published online by Cambridge University Press:  09 April 2009

K. I. Beidar
Affiliation:
Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan, e-mail: [email protected]
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Poland e-mail: [email protected]
R. Wiegandt
Affiliation:
Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary e-mail: [email protected]
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Abstract

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We prove that polynomial rings in one indeterminate over nil rings are antiregular radical and uniformly strongly prime radical. These give some approximations of Köthe's problem. We also study the uniformly strongly prime and superprime radicals of polynomial rings in non-commuting indeterminates. Moreover, we show that the semi-uniformly strongly prime radical coincides with the uniformly strongly prime radical and that the class of semi-superprime rings is closed under taking finite subdirect sums.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

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