经典Baer结果在泊松代数中的推广

IF 0.3 Q4 MATHEMATICS, APPLIED Algebra & Discrete Mathematics Pub Date : 2021-04-10 DOI:10.12958/ADM1758

L. A. Kurdachenko, A. A. Pypka, I. Subbotin

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引用次数: 0

摘要

本文证明了如果P是泊松代数，并且P的第n个超中心（中心）具有有限余维，则P包含有限维理想K，使得P/K是幂零（阿贝尔）。作为推论，我们证明了如果泊松代数P（在某个特定域上）的第n个超中心具有有限余维，并且P不包含零除数，那么P是阿贝尔代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On extension of classical Baer results to Poisson algebras

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 nth 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.

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