On the factorization of the polynomials \(X^{p^{2r}+p^{r+1}}-aX^{p^ r+1}-bX-c\) over the finite fields \({\mathbb{F}}_{p^ s}\).
type: Item
instance of: scholarly article
title: On the factorization of the polynomials \(X^{p^{2r}+p^{r+1}}-aX^{p^ r+1}-bX-c\) over the finite fields \({\mathbb{F}}_{p^ s}\).
zbMATH Open document ID: 0628.12011
DOI: 10.1007/BF01169088
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155216
review text: The polynomials in the title are studied with regard to irreducibility and hyponormality [for the latter notion see, e.g., the author, Acta Arith. 39, 105-111 (1981; Zbl 0494.12014)]. Earlier results are improved and generalized, e.g., a classical result of \textit{Ø. Ore} [Trans. Am. Math. Soc.36, 243-274 (1934; Zbl 0009.10003)] for the case \(r=s\). The detailed statements of the theorems are rather complicated, so they cannot be reproduced here.
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 4021283
zbMATH Keywords: polynomials over finite fields
zbMATH Keywords: irreducibility
zbMATH Keywords: hyponormality
author: Simon Joseph Agou
MaRDI profile type: Publication
cites work: Sur la factorisation des polynômes \(f(X^{p^{2r}}-aX^{p^r}-bX)\) sur un corps fini \(\mathbb{F}_{p^s}\)
cites work: Degre minimum des polynômes \(f(\sum_{i=O,\dots ,m} a_ iX^{p^{ri}}\) sur les corps finis de caractéristique \(p>m\)
cites work: Sur l'irréductibilité des trinômes $X^{p^r + 1} - aX - b$ sur les corps finis $F_{p^s}$
cites work: The Degrees of the Factors of Certain Polynomials Over Finite Fields
cites work: On the Theorem of Gleason and Marsh
description: scientific article; zbMATH DE number 4021283