A discriminant criteria for reducibility of a polynomial
type: Item
instance of: scholarly article
title: A discriminant criteria for reducibility of a polynomial
zbMATH Open document ID: 0601.12006
DOI: 10.1007/BF02764873
author: S. Friedland
author: Michael D. Fried
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The authors consider sufficient conditions for a polyomial \(p(w)\) over a domain \(K\) (a commutative ring without zero divisors) with unity to split into linear factors in \(K\), and intend to generalize the Motzkin-Taussky theorem to the case \(K={\mathbb{C}}[z]\) or \({\mathbb{Z}}\) [cf. \textit{T. S. Motzkin} and \textit{O. Taussky}, Trans. Am. Math. Soc. 80, 387-401 (1955; Zbl 0067.25401)]. For this purpose, they use the Riemann-Hurwitz formula (in case of \(K={\mathbb{C}}[z])\) and a theorem of Minkowski (in case of \(K={\mathbb{Z}})\), and obtain an additional condition on the roots of \(p(w)\) which together with the discriminant condition implies the splitting of \(p(w)\).
reviewed by: Hideo Yokoi
Mathematics Subject Classification ID: 11R09
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 3968704
zbMATH Keywords: splitting of polynomial
zbMATH Keywords: Motzkin-Taussky theorem
zbMATH Keywords: Riemann-Hurwitz formula
zbMATH Keywords: discriminant condition
MaRDI profile type: Publication
cites work: Q3931656
cites work: On a theorem of Ritt and related Diophantine problems.
cites work: Simultaneous similarity of matrices
cites work: Pairs of Matrices With Property L. II
cites work: Q5723265
cites work: Q5682591
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description: scientific article; zbMATH DE number 3968704