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arXiv · 1610.02321

On Polynomial Rings Over Nil Rings in Several Variables and the Central Closure of Prime Nil Rings

Mikhail Chebotar·Wen-Fong Ke·Pjek-Hwee Lee·Edmund R. Puczylowski
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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 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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Mikhail Chebotar, Wen-Fong Ke, Pjek-Hwee Lee, Edmund R. Puczylowski. 2016-10-07. On Polynomial Rings Over Nil Rings in Several Variables and the Central Closure of Prime Nil Rings. https://doi.org/10.1007/s11856-017-1616-6

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