On the generalized difference polynomials
type: Item
instance of: scholarly article
title: On the generalized difference polynomials
zbMATH Open document ID: 0689.12013
author: Laurenţiu Panaitopol
author: Doru Ştefănescu
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Factorization properties of a class of polynomials F in two indeterminates with the coefficients in an algebraically closed field are investigated. This class includes the generalized difference polynomials considered by \textit{L. A. Rubel} and \textit{S. S. Abhyankar} [J. Indian Math. Soc., New Ser. 43, 69-78 (1979; Zbl 0532.12021)] and by \textit{L. A. Rubel}, \textit{A. Schinzel} and \textit{H. Tverberg} [J. Number Theory 12, 230-235 (1980; Zbl 0435.12009)]. A rational number \(p_ Y(F)\) associated with the polynomial \(F\in k[X,Y]\) is introduced and some properties of \(p_ Y(F)\) using a Newton polygon argument are established. New irreducibility criteria for polynomials in two variables with the coefficients in an algebraically closed field are deduced and new proofs for the irreducibility criteria of A. Ehrenfeucht and G. Angermüller are obtained.
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 11R09
zbMATH DE Number: 4128944
zbMATH Keywords: generalized difference polynomials
zbMATH Keywords: Newton polygon
zbMATH Keywords: irreducibility criteria
MaRDI profile type: Publication
full work available at URL: pjm.1990.143.341
OpenAlex ID: W1975903181
DOI: 10.2140/PJM.1990.143.341
description: scientific article; zbMATH DE number 4128944