Geodesic
On extension of classical Baer results to Poisson algebras
Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 84-108

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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.
Keywords: Lie algebra, ideal, center, hypercenter, zero divisor, finite dimension, nilpotency.
Mots-clés : Poisson algebra, subalgebra 
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     author = {L. A. Kurdachenko and A. A. Pypka and I. Ya. Subbotin},
     title = {On extension of classical {Baer} results to {Poisson} algebras},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a5/}
}
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L. A. Kurdachenko; A. A. Pypka; I. Ya. Subbotin. On extension of classical Baer results to Poisson algebras. Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 84-108. http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a5/