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періодичних видань НАН України
On extension of classical Baer results to Poisson algebras
Репозиторій DSpace/Manakin
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On extension of classical Baer results to Poisson algebras
Інший ID:
DOI:10.12958/adm1758
2020 MSC: 17B63,17B65.
2020 MSC: 17B63,17B65.
Посилання:
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.
Підтримка:
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).
Дата:
2021
Переглядів:
227
Завантажень:
144
Анотація:
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.
