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

doi:10.1007/s11856-017-1616-6

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Pages (from-to)	309-322
Number of pages	14
Journal	Israel Journal of Mathematics
Volume	223
Issue number	1
DOIs	https://doi.org/10.1007/s11856-017-1616-6
Publication status	Published - 2018 Feb 1

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-017-1616-6

Cite this

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N2 - 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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On polynomial rings over nil rings in several variables and the central closure of prime nil rings

Abstract

All Science Journal Classification (ASJC) codes

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