Key polynomials and minimal pairs

2017/11/12 by Novacoski, Josnei · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.04296

Abstract

In this paper we establish the relation between key polynomials (as defined in \citeSopivNova) 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 ν is equal to its truncation on some polynomial if and only if ν is valuation-transcendental. Another important result of this paper is that if μ is any extension of ν to K[x] and Λ is a complete sequence of key polynomials for ν, without last element, then for each Q∈ Λ there exists a suitable root a_Q∈ K of Q such that \a_Q\_{Q∈ Λ} is a pseudo-convergent sequence defining μ.

Cited by

• On the distances of an element to its conjugates

Related

• Extensions of a valuation from K to K[x]
• Key polynomials and pseudo-convergent sequences
• On truncations of valuations
• Key Polynomials
• Minimal limit key polynomials