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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| Дата: | 2021 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2021
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188679 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188679 |
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dspace |
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irk-123456789-1886792023-03-12T01:28:50Z On extension of classical Baer results to Poisson algebras Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. 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. 2021 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188679 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. |
| spellingShingle |
Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. On extension of classical Baer results to Poisson algebras Algebra and Discrete Mathematics |
| author_facet |
Kurdachenko, L.A. Pypka, A.A. Subbotin I.Ya. |
| author_sort |
Kurdachenko, L.A. |
| title |
On extension of classical Baer results to Poisson algebras |
| title_short |
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_sort |
on extension of classical baer results to poisson algebras |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2021 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188679 |
| 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. |
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Algebra and Discrete Mathematics |
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AT kurdachenkola onextensionofclassicalbaerresultstopoissonalgebras AT pypkaaa onextensionofclassicalbaerresultstopoissonalgebras AT subbotiniya onextensionofclassicalbaerresultstopoissonalgebras |
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2023-10-18T23:08:54Z |
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2023-10-18T23:08:54Z |
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