On Polynomial Rings Over Nil Rings in Several Variables and the Central Closure of Prime Nil Rings
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
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| _version_ | 1866929427979436032 |
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| author | Chebotar, Mikhail Ke, Wen-Fong Lee, Pjek-Hwee Puczylowski, Edmund R. |
| author_facet | Chebotar, Mikhail Ke, Wen-Fong Lee, Pjek-Hwee Puczylowski, Edmund R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_02321 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On Polynomial Rings Over Nil Rings in Several Variables and the Central Closure of Prime Nil Rings Chebotar, Mikhail Ke, Wen-Fong Lee, Pjek-Hwee Puczylowski, Edmund R. Rings and Algebras 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. |
| title | On Polynomial Rings Over Nil Rings in Several Variables and the Central Closure of Prime Nil Rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/1610.02321 |