On prolongations of valuations via Newton polygons and liftings of polynomials

DOI10.1016/j.jpaa.2012.03.034zbMath1267.12004OpenAlexW2052533483MaRDI QIDQ1940198

Sanjeev Kumar, Sudesh Kaur Khanduja

Publication date: 6 March 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2012.03.034

zbMATH Keywords

Newton polygonsTranscendental extensionValuations

Mathematics Subject Classification ID

Polynomials in general fields (irreducibility, etc.) (12E05) Non-Archimedean valued fields (12J25) Valued fields (12J10)

Related Items (16)

Discriminant and integral basis of quintic fields defined by x5 + ax + b ⋮ On non-monogenity of the number fields defined by certain quadrinomials ⋮ Reformulation of Hensel's lemma and extension of a theorem of Ore ⋮ Non-monogenity of certain octic number fields defined by trinomials ⋮ Nonmonogenity of number fields defined by trinomials ⋮ On factorization of polynomials in henselian valued fields ⋮ Discriminant and integral basis of sextic fields defined by x6+ax+b ⋮ On nonmonogenic number fields defined by ⋮ A note on non-monogenity of number fields arised from sextic trinomials ⋮ On nonmonogenic algebraic number fields ⋮ Abstract key polynomials and distinguished pairs ⋮ A generalization of a theorem of Ore ⋮ On the index theorem of Ore ⋮ On the index of an algebraic integer and beyond ⋮ On the discriminant of pure number fields ⋮ Common index divisor of the number fields defined by

Cites Work

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• A theorem of characterization of residual transcendental extensions of a valuation
• A generalization of Eisenstein-Schönemann irreducibility criterion
• Minimal pairs of definition of a residual transcendental extension of a valuation
• Roots of generalized Schönemann polynomials in Henselian extension fields
• On the structure of the irreducible polynomials over local fields
• Prolongations of valuations to finite extensions
• A Generalization of Dedekind Criterion
• The Ruled Residue Theorem for Simple Transcendental Extensions of Valued Fields
• Factorization over local fields and the irreducibility of generalized difference polynomials
• On extensions generated by roots of lifting polynomials
• Newton polygons of higher order in algebraic number theory
• Valued Fields

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