Non-characteristic approximate roots of polynomials
type: Item
instance of: scholarly article
title: Non-characteristic approximate roots of polynomials
zbMATH Open document ID: 1270.13004
published in: Journal of Algebra
publication date: 2012-02-11T00:00:00Z
review text: Let \(K\) be a field and \(K((X))\) the Laurent series in the variable \(X\) with coefficients in \(K\). Let \(f(Y)\in K((X))[Y]\) be a monic and irreducible polynomial. For any positive integer \(l\) dividing \(\deg_Yf\) the approximate \(l-th\) root of \(f\) is a monic polynomial \(g(Y)\in K((X))[Y]\) such that \(\deg_Y(f-g^l) < \deg_Yf -{\deg_Yf\over l}\). The approximate \(l\)-th root exists and is uniquely determined. In this paper, the author extends Abhyankar-Moh results about this notion known in the case of characteristic degree to the case of non characteristic degree.
reviewed by: Ali Benhissi
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13J05
zbMATH DE Number: 6005461
zbMATH Keywords: Approximate roots of polynomials
zbMATH Keywords: characteristic sequences
author: Szymon Brzostowski
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.06.030
OpenAlex ID: W2009532897
cites work: Q3215049
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DOI: 10.1016/J.JALGEBRA.2011.06.030
description: scientific article; zbMATH DE number 6005461