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Limit key polynomials as p-polynomials
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-03-31 , DOI: 10.1016/j.jalgebra.2021.03.024
Michael de Moraes , Josnei Novacoski

The main goal of this paper is to characterize limit key polynomials for a valuation ν on K[x]. We consider the set Ψα of key polynomials for ν of degree α. We set p to be the exponent characteristic of ν. Our first main result (Theorem 1.1) is that if F is a limit key polynomial for Ψα, then the degree of F is prα for some rN. Moreover, in Theorem 1.2, we show that there exist QΨα and F a limit key polynomial for Ψα, such that the Q-expansion of F only has terms which are powers of p.



中文翻译:

限关键字多项式为p -polynomials

本文的主要目的是为极限ν刻画极限键多项式的特征。ķ[X]。我们考虑一套Ψα的关键多项式ν度的α。我们将p设为ν的指数特征。我们的第一个主要结果(定理1.1)是,如果FΨα,则F的度为p[Rα 对于一些 [Rñ。而且,在定理1.2中,我们证明存在ΨαF为的极限键多项式Ψα,使得FQ展开仅具有p的幂的项。

更新日期:2021-04-02
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