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 algeb...
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| Дата: | 2021 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2021
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1758 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543139413622784 |
|---|---|
| author | Kurdachenko, L. A. Pypka, A. A. Subbotin, I. Ya. |
| author_facet | Kurdachenko, L. A. Pypka, A. A. Subbotin, I. Ya. |
| author_sort | Kurdachenko, L. A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-04-11T06:11:31Z |
| 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 | 2026-02-08T07:58:29Z |
| format | Article |
| id | admjournalluguniveduua-article-1758 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:29Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-17582021-04-11T06:11:31Z On extension of classical Baer results to Poisson algebras Kurdachenko, L. A. Pypka, A. A. Subbotin, I. Ya. Poisson algebra, Lie algebra, subalgebra, ideal, center, hypercenter, zero divisor, finite dimension, nilpotency 17B63, 17B65 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. Lugansk National Taras Shevchenko University National Research Foundation of Ukraine 2021-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1758 10.12958/adm1758 Algebra and Discrete Mathematics; Vol 31, No 1 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1758/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1758/821 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | Poisson algebra Lie algebra subalgebra ideal center hypercenter zero divisor finite dimension nilpotency 17B63 17B65 Kurdachenko, L. A. Pypka, A. A. Subbotin, I. Ya. On extension of classical Baer results to Poisson algebras |
| 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 |
| topic | Poisson algebra Lie algebra subalgebra ideal center hypercenter zero divisor finite dimension nilpotency 17B63 17B65 |
| topic_facet | Poisson algebra Lie algebra subalgebra ideal center hypercenter zero divisor finite dimension nilpotency 17B63 17B65 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1758 |
| work_keys_str_mv | AT kurdachenkola onextensionofclassicalbaerresultstopoissonalgebras AT pypkaaa onextensionofclassicalbaerresultstopoissonalgebras AT subbotiniya onextensionofclassicalbaerresultstopoissonalgebras |