On analogs of some classical group-theoretic results in Poisson algebras - Kurdachenko, L.A.; Pypka, A.A.; Subbotin, I.Ya. (Reports of the National Academy of Sciences of Ukraine, 2021)
We investigate the Poisson algebras, in which the n-th hypercenter (center) has a finite codimension. It was established that, in this case, the Poisson algebra P includes a finite-dimensional ideal K such that P/K is nilpotent (Abelian). Moreover, if the n-th hypercenter of a Poisson algebra P over some field has a finite codimension, and if P does not contain zero divisors, then P is Abelian.