Solvability of Poisson algebras

Let P be a Poisson algebra with Lie bracket {,} over field F of characteristic p≥0. In this paper, the structure is investigated. particular, if solvable respect to its bracket, then we prove that ideal J generated by all elements {{{x1,x2},{x3,x4}},x5} x1,…,x5∈P associative nilpotent index bounded function derived length P. We use result further and p≠2, {P,P}P nil.