Reducibility of polynomials in several variables. II
type: Item
instance of: scholarly article
title: Reducibility of polynomials in several variables. II
zbMATH Open document ID: 0571.12011
author: Andrzej Schinzel
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pjm/1102706460
review text: Let \(f_ i(x)\) be non-constant rational functions over a field K \((i=1,2,...)\). A necessary and sufficient condition is given for reducibility over K of the numerator of the sum \(\sum^{n}_{i=1}f_ i(x_ i)\) in its reduced form provided \(n\geq 3\). If char \(K\neq 2\) the condition is simple and if char K\(=0\) it is never satisfied. This generalizes the results of A. Ehrenfeucht and A. Pełczyński and of \textit{H. Tverberg} concerning polynomials [see Pr. Mat. 8, 117-118 (1964; Zbl 0125.284); Q. J. Math., Oxf. II. Ser. 17, 364-366 (1966; Zbl 0145.048)]. The method is similar to that used in Part I [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 11, 633-638 (1963; Zbl 0122.019)]. A proof for the case char \(K\neq 2\) using a different method has since been found by \textit{M. Fried} [Irreducibility results for separated variables equations, to appear in J. Pure Appl. Algebra].
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 3910513
zbMATH Keywords: irreducibility
zbMATH Keywords: rational functions
zbMATH Keywords: polynomials
Wikidata QID: Q105962211
MaRDI profile type: Publication
OpenAlex ID: W1983611453
DOI: 10.2140/PJM.1985.118.531
description: scientific article; zbMATH DE number 3910513