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http://dx.doi.org/10.4134/JKMS.2005.42.5.1003

NILRADICALS OF POWER SERIES RINGS AND NIL POWER SERIES RINGS  

HUH, CHAN (Department of Mathematics, Pusan National University)
KIM, CHOL ON (Department of Mathematics, Pusan National University)
KIM, EUN JEONG (Department of Mathematics, Pusan National University)
KIM, HONG KEE (Department of Mathematics, Gyungsang National University)
LEE, YANG (Department of Mathematics, Pusan National University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.5, 2005 , pp. 1003-1015 More about this Journal
Abstract
Klein proved that polynomial rings over nil rings of bounded index are also nil of bounded index; while Puczylowski and Smoktunowicz described the nilradical of a power series ring with an indeterminate. We extend these results to those with any set of commuting indeterminates. We also study prime radicals of power series rings over some class of rings containing the case of bounded index, finding some examples which elaborate our arguments; and we prove that R is a PI ring of bounded index then the power series ring R[[X]], with X any set of indeterminates over R, is also a PI ring of bounded index, obtaining the Klein's result for polynomial rings as a corollary.
Keywords
nilradical; Wedderburn radical; polynomial ring; power series ring; nil ring of bounded index;
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Times Cited By Web Of Science : 1  (Related Records In Web of Science)
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