Israel Journal of Mathematics

, Volume 223, Issue 1, pp 309–322 | Cite as

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

  • M. ChebotarEmail author
  • W.-F. Ke
  • P.-H. Lee
  • E. R. Puczyłowski


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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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • M. Chebotar
    • 1
    Email author
  • W.-F. Ke
    • 2
  • P.-H. Lee
    • 3
  • E. R. Puczyłowski
    • 4
  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA
  2. 2.Department of Mathematics and Research Center for Theoretical SciencesNational Cheng Kung UniversityTainan 701Taiwan
  3. 3.Department of MathematicsNational Taiwan University and National Center for Theoretical SciencesTaipei 106Taiwan
  4. 4.Institute of MathematicsUniversity of WarsawWarsawPoland

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