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arXiv · 2104.08609

On truncations of valuations

Josnei Antonio Novacoski·Caio Henrique Silva de Souza
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Abstract

In this paper we study the truncation $\nu_q$ of a valuation $\nu$ on a polynomial $q$. It is known that when $q$ is a key polynomial, then $\nu_q$ is a valuation. It is also known that the converse does not hold. We show that when $q$ is a key polynomial, then $\nu_q$ is the restriction of the truncation given by an optimizing root of $q$. We also discuss which conditions assure that $\nu_q=\nu$. Finally, we assume that $\nu_q$ is a valuation and present some conditions, given in terms of the graded algebra, to assure that $q$ is a key polynomial.

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Josnei Antonio Novacoski, Caio Henrique Silva de Souza. 2021-04-17. On truncations of valuations. https://arxiv.org/abs/2104.08609

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