On extension of classical Baer results to Poisson algebras
In this paper we prove that if P is a Poisson algebra and the n-th hypercenter (center) of P has a finite codimension, then P includes a finite-dimensional ideal K such that P/K is nilpotent (abelian). As a corollary, we show that if the n-th hypercenter of a Poisson algebra P (over some specific fi...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2021 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188679 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On extension of classical Baer results to Poisson algebras / L.A. Kurdachenko, A.A. Pypka, I.Ya. Subbotin // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 84–108. — Бібліогр.: 52 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730974902616064 |
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| author | Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. |
| author_facet | Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. |
| citation_txt | On extension of classical Baer results to Poisson algebras / L.A. Kurdachenko, A.A. Pypka, I.Ya. Subbotin // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 84–108. — Бібліогр.: 52 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper we prove that if P is a Poisson algebra and the n-th hypercenter (center) of P has a finite codimension, then P includes a finite-dimensional ideal K such that P/K is nilpotent (abelian). As a corollary, we show that if the n-th hypercenter of a Poisson algebra P (over some specific field) has a finite codimension and P does not contain zero divisors, then P is an abelian algebra.
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| first_indexed | 2025-12-07T19:23:32Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188679 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:23:32Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. 2023-03-11T13:22:53Z 2023-03-11T13:22:53Z 2021 On extension of classical Baer results to Poisson algebras / L.A. Kurdachenko, A.A. Pypka, I.Ya. Subbotin // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 84–108. — Бібліогр.: 52 назв. — англ. 1726-3255 DOI:10.12958/adm1758 2020 MSC: 17B63,17B65. https://nasplib.isofts.kiev.ua/handle/123456789/188679 In this paper we prove that if P is a Poisson algebra and the n-th hypercenter (center) of P has a finite codimension, then P includes a finite-dimensional ideal K such that P/K is nilpotent (abelian). As a corollary, we show that if the n-th hypercenter of a Poisson algebra P (over some specific field) has a finite codimension and P does not contain zero divisors, then P is an abelian algebra. Dedicated to the 60th anniversary of the Department of Algebra and Mathematical Logic of Taras Shevchenko National University of Kyiv
 The first two authors are supported by the National Research Foundation of Ukraine (grant no. 2020.02/0066). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On extension of classical Baer results to Poisson algebras Article published earlier |
| spellingShingle | On extension of classical Baer results to Poisson algebras Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. |
| title | On extension of classical Baer results to Poisson algebras |
| title_full | On extension of classical Baer results to Poisson algebras |
| title_fullStr | On extension of classical Baer results to Poisson algebras |
| title_full_unstemmed | On extension of classical Baer results to Poisson algebras |
| title_short | On extension of classical Baer results to Poisson algebras |
| title_sort | on extension of classical baer results to poisson algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188679 |
| work_keys_str_mv | AT kurdachenkola onextensionofclassicalbaerresultstopoissonalgebras AT pypkaaa onextensionofclassicalbaerresultstopoissonalgebras AT subbotiniya onextensionofclassicalbaerresultstopoissonalgebras |