Indecomposability of polynomials via Jacobian matrix
type: Item
instance of: scholarly article
title: Indecomposability of polynomials via Jacobian matrix
zbMATH Open document ID: 1202.13014
published in: Journal of Algebra
publication date: 2010-07-20T00:00:00Z
review text: A multivariate polynomial is called decomposable if it can be written as a composition of a univariate polynomial of degree \(\geq 2\) and a multivariate polynomial. In the first section, deomposability is characterized by a rank condition of the so-called Jacobi-matrix of the polynomial. For characteristic zero, this criterion can be found in [\textit{Y. Stein}, Isr. J. Math. 68, No. 1, 109--122 (1989; Zbl 0716.12001)]. Here the result is generalized to positive characteristics. Based on this criterion, some classes of polynomials are shown to be indecomposable.
reviewed by: Josef Schicho
Mathematics Subject Classification ID: 13P05
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 5758103
zbMATH Keywords: indecomposable polynomials
zbMATH Keywords: Noether's theorem
zbMATH Keywords: Bertini's theorem
zbMATH Keywords: Ostrowski's theorem
zbMATH Keywords: Newton's polygon
author: Guillaume Chèze
author: Salah Najib
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.01.007
OpenAlex ID: W2062228305
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DOI: 10.1016/J.JALGEBRA.2010.01.007
description: scientific article; zbMATH DE number 5758103