Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2005.09.01
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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.

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References

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  1. Arnold's Theorem on the Strongly Finite Type (SFT) Property and the Dimension of Power Series Rings vol.43, pp.1, 2015, https://doi.org/10.1080/00927872.2014.897590
  2. Rings Whose Nilpotent Elements form a Levitzki Radical Ring vol.35, pp.4, 2007, https://doi.org/10.1080/00927870601117597
  3. On nilpotent elements of ore extensions vol.10, pp.03, 2017, https://doi.org/10.1142/S1793557117500437