Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Ratseev S. M. On Poisson Customary Polynomial Identities. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 2, pp. 150-155. DOI: 10.18500/1816-9791-2014-14-2-150-155

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On Poisson Customary Polynomial Identities

Ratseev Sergey Mihailovich, Ulyanovsk State University

We study Poisson customary and Poisson extended customary polynomials. We show that the sequence of codimensions {rn(V )}n¸1 of every extended customary space of variety V of Poisson algebras over an arbitrary field is either bounded by a polynomial or at least exponential. Furthermore, if this sequence is bounded by polynomial then there is a polynomial R(x) with rational coefficients such that rn(V ) = R(n) for all sufficiently large n. We present lower and upper bounds for the polynomials R(x) of an arbitrary fixed degree.

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