On prolongations of valuations via Newton polygons and liftings of polynomials
type: Item
instance of: scholarly article
title: On prolongations of valuations via Newton polygons and liftings of polynomials
zbMATH Open document ID: 1267.12004
author: Sudesh Kaur Khanduja
author: Sanjeev Kumar
published in: Journal of Pure and Applied Algebra
publication date: 2013-03-06T00:00:00Z
review text: Let \((K,v)\) be a real valued field and \(K(\theta)\) be a finite separable extension of \(K\) with \(\theta\) integral over \(R_v\), the valuation ring of \(v\).The scope of the paper is the description of all prolongations of \(v\) to \(K(\theta)\). This problem is classical but the method in the paper is new. It involves Newton polygons as well as prolongations of \(v\) to a simple transcendental extension \(K(X)\) of \(K\) whose residue field are transcendental over \(K_v\), the residue field of \(v\). The residue field of such a prolongation \(w\) is a simple transcendental extension \(\bar L(Z)\) of a finite extension \(\bar L\) of \(K_v\). The method in the present paper uses also liftings of polynomials belonging to \(\bar L[Z]\) with respect to \(w\) which yield suitable polynomials over \(K\). The authors end the paper by deducing some classical theorems on the subject.
reviewed by: Ali Benhissi
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 12J25
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 6141852
zbMATH Keywords: Valuations
zbMATH Keywords: Newton polygons
zbMATH Keywords: Transcendental extension
MaRDI profile type: Publication
full work available at URL: j.jpaa.2012.03.034
OpenAlex ID: W2052533483
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DOI: 10.1016/J.JPAA.2012.03.034
description: scientific article; zbMATH DE number 6141852