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On polynomial rings over nil rings in several variables and the central closure of prime nil rings

Israel Journal of Mathematics volume 223, pages 309–322 (2018)Cite this article

Abstract

We prove that the ring of polynomials in several commuting indeterminates over a nil ring cannot be homomorphically mapped onto a ring with identity, i.e. it is Brown-McCoy radical. It answers a question posed by Puczyłowski and Smoktunowicz. We also show that the central closure of a prime nil ring cannot be a simple ring with identity, solving a problem due to Beidar.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    M. Chebotar

  2. Department of Mathematics and Research Center for Theoretical Sciences, National Cheng Kung University, Tainan 701, Taiwan

    W.-F. Ke

  3. Department of Mathematics, National Taiwan University and National Center for Theoretical Sciences, Taipei 106, Taiwan

    P.-H. Lee

  4. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    E. R. Puczyłowski

Authors
  1. M. Chebotar
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  2. W.-F. Ke
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  3. P.-H. Lee
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  4. E. R. Puczyłowski
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Corresponding author

Correspondence to M. Chebotar.

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Chebotar, M., Ke, WF., Lee, PH. et al. On polynomial rings over nil rings in several variables and the central closure of prime nil rings. Isr. J. Math. 223, 309–322 (2018). https://doi.org/10.1007/s11856-017-1616-6

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  • DOI: https://doi.org/10.1007/s11856-017-1616-6

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