On the decomposition of \(x^d + a_ex^e +\dots +a_1x +a_0\)
type: Item
instance of: scholarly article
title: On the decomposition of \(x^d + a_ex^e +\dots +a_1x +a_0\)
zbMATH Open document ID: 0990.11076
DOI: 10.1155/S0161171200002830
author: Javier Gomez-Calderon
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-20T00:00:00Z
full work available at URL: https://eudml.org/doc/49300
review text: The author calls \(f(x)\in K[x]\) (for a field \(K\)) decomposable over \(K\) if \(f(x)= g(h(x))\) for some \(g(x),h(x)\in K[x]\) with \(1<\deg(h)< \deg(F)\) and indecomposable otherwise. Moreover, if \(f(x)= g(x^m)\) for \(m>1\), then \(f\) is called trivially decomposable. He shows that if \(e\) is the largest proper divisor of \(d\), then \(x^d+ a_{d-e-1}+ \cdots+ a_1x+a_0\) is either indecomposable or trivially decomposable. Results on Dickson polynomials are also presented.
reviewed by: Richard A. Mollin
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 1501978
zbMATH Keywords: trivially decomposable polynomials
zbMATH Keywords: Dickson polynomials
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1501978