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

  • M. Chebotar
  • 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 Puczylowski 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 2017

Authors and Affiliations

  • M. Chebotar
    • 1
  • 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 UniversityTainanTaiwan
  3. 3.Department of MathematicsNational Taiwan University and National Center for Theoretical SciencesTaipeiTaiwan
  4. 4.Institute of MathematicsUniversity of WarsawWarsawPoland

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