On analogs of some classical group-theoretic results in Poisson algebras
DOI:
https://doi.org/10.15407/dopovidi2021.03.011Keywords:
Poisson algebra, center, hypercenter, zero divisors, nilpotencyAbstract
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.
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