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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Опубліковано в: :Algebra and Discrete Mathematics
Дата:2021
Автори: Kurdachenko, L.A., Pypka, A.A., Subbotin I.Ya.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут прикладної математики і механіки НАН України 2021
Онлайн доступ:https://nasplib.isofts.kiev.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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2025-12-07T19:23:32Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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
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AT pypkaaa onextensionofclassicalbaerresultstopoissonalgebras
AT subbotiniya onextensionofclassicalbaerresultstopoissonalgebras