Key polynomials and minimal pairs

JOURNAL OF ALGEBRA

卷:523

Article

Novacoski, Josnei¹ 

[1] Univ Fed Sao Carlos, Dept Matemat, Rodovia Washington Luis 235, BR-13565905 Sao Carlos, SP, Brazil

关键词: Local uniformization;    Key polynomials;    Minimal pairs;   

DOI  :  10.1016/j.jalgebra.2018.12.022

来源: Elsevier

【 摘 要 】

In this paper we establish the relation between key polynomials (as defined in [12]) and minimal pairs of definition of a valuation. We also discuss truncations of valuations on a polynomial ring K[x]. We prove that a valuation nu is equal to its truncation on some polynomial if and only if nu is valuation-transcendental. Another important result of this paper is that if mu is any extension of nu to (K) over bar [x] and Lambda is a complete sequence of key polynomials for nu, without last element, then for each Q is an element of Lambda there exists a suitable root a(Q) is an element of (K) over bar of Q such that {a(Q)}(Q is an element of Lambda) is a pseudo-convergent sequence defining mu. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free