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Radicals and polynomial rings

Part of: Radicals and radical properties of rings

Published online by Cambridge University Press:  09 April 2009

K. I. Beidar ,
E. R. Puczyłowski  and
R. Wiegandt
K. I. Beidar
Affiliation:
Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan, e-mail: beidar@mail.ncku.edu.tw
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Poland e-mail: edmundp@mimuw.edu.pl
R. Wiegandt
Affiliation:
Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary e-mail: wiegandt@math-inst.hu
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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.

MSC classification

Secondary: 16N20: Jacobson radical, quasimultiplication 16N40: Nil and nilpotent radicals, sets, ideals, rings 16N80: General radicals and rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 23 - 32
Copyright
Copyright © Australian Mathematical Society 2002

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