On extension of classical Baer results to Poisson algebras

• Published in: Algebra and Discrete Mathematics
• Date: 2021
• Main Authors: Kurdachenko, L.A., Pypka, A.A., Subbotin I.Ya.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188679
• 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.

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...