On Newton polygons techniques and factorization of polynomials over Henselian fields

DOI10.1142/S0219498820501881zbMath1446.13004WikidataQ114614561 ScholiaQ114614561MaRDI QIDQ5133837

Lhoussain El Fadil

Publication date: 11 November 2020

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

Newton polygonvalued fieldsprime ideal factorizationHenselizationtheorem of the polygontheorem of the residual polynomial

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18)

Related Items (18)

On power integral bases of certain pure number fields defined by \(x^{42}-m\) ⋮ On common index divisors and monogenity of certain number fields defined by x⁵ + ax² + b ⋮ On power integral bases of certain pure number fields defined by $x^{3^r\cdot 7^s}-m$ ⋮ On non monogenity of certain number fields defined by trinomials \(x^6 + ax^3 + b\) ⋮ On power integral bases of certain pure number fields defined by $x^{84}-m$ ⋮ On monogenity of certain pure number fields defined by $x^{2^r\cdot7^s}-m$ ⋮ On index and monogenity of certain number fields defined by trinomials ⋮ A generalization of Eisenstein-Schönemann's irreducibility criterion ⋮ Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9 ⋮ On the geometric determination of extensions of non-Archimedean absolute values ⋮ On power integral bases for certain pure number fields defined by x2r.5s−m ⋮ On monogenity of certain pure number fields defined by xpr − m ⋮ On integral bases and monogeneity of pure sextic number fields with non-squarefree coefficients ⋮ Factorization of polynomials over valued fields based on graded polynomials ⋮ On monogenity of certain pure number fields defined by \(x^{20}-m\) ⋮ On power integral bases of certain pure number fields defined by \(x^{3^r} - m\) ⋮ On monogenity of certain number fields defined by trinomials ⋮ On power integral bases for certain pure number fields defined by $x^{2\cdot 3^k}-m$

Cites Work

• Unnamed Item
• A generalization of a theorem of Ore
• Factorization over local fields and the irreducibility of generalized difference polynomials
• ON IRREDUCIBLE FACTORS OF POLYNOMIALS OVER COMPLETE FIELDS
• On the extensions of discrete valuations in number fields
• Newton polygons of higher order in algebraic number theory

This page was built for publication: On Newton polygons techniques and factorization of polynomials over Henselian fields