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

M. Chebotar, Wen-Fong Ke, P. H. Lee, E. R. Puczyłowski

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)309-322
Number of pages14
JournalIsrael Journal of Mathematics
Volume223
Issue number1
DOIs
Publication statusPublished - 2018 Feb 1

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Nil
Several Variables
Polynomial ring
Closure
Ring
Polynomial

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On polynomial rings over nil rings in several variables and the central closure of prime nil rings. / Chebotar, M.; Ke, Wen-Fong; Lee, P. H.; Puczyłowski, E. R.

In: Israel Journal of Mathematics, Vol. 223, No. 1, 01.02.2018, p. 309-322.

Research output: Contribution to journalArticle

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