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NILRADICALS OF POWER SERIES RINGS AND NIL POWER SERIES RINGS
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 Title & Authors
NILRADICALS OF POWER SERIES RINGS AND NIL POWER SERIES RINGS
HUH, CHAN; KIM, CHOL ON; KIM, EUN JEONG; KIM, HONG KEE; LEE, YANG;
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 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;
 Language
English
 Cited by
1.
Arnold's Theorem on the Strongly Finite Type (SFT) Property and the Dimension of Power Series Rings, Communications in Algebra, 2015, 43, 1, 337  crossref(new windwow)
2.
Rings Whose Nilpotent Elements form a Levitzki Radical Ring, Communications in Algebra, 2007, 35, 4, 1379  crossref(new windwow)
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