A generalization of Eisenstein-Schönemann irreducibility criterion

DOI10.1007/s00229-010-0393-xzbMath1222.12002OpenAlexW2073808753MaRDI QIDQ617840

Sudesh Kaur Khanduja, Ramneek Khassa

Publication date: 14 January 2011

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-010-0393-x

zbMATH Keywords

PolynomialsEisenstein-Schönemann irreducibility criterion

Mathematics Subject Classification ID

Special polynomials in general fields (12E10) Non-Archimedean valued fields (12J25) Valued fields (12J10)

Related Items (11)

Reformulation of Hensel's lemma and extension of a theorem of Ore ⋮ A Generalization of the Eisenstein–Dumas–Schönemann Irreducibility Criterion ⋮ On prolongations of valuations via Newton polygons and liftings of polynomials ⋮ THE MAIN INVARIANT OF A DEFECTLESS POLYNOMIAL ⋮ ON IRREDUCIBLE FACTORS OF POLYNOMIALS OVER COMPLETE FIELDS ⋮ On the index theorem of Ore ⋮ On Brown polynomials ⋮ ON LIFTINGS OF POWERS OF IRREDUCIBLE POLYNOMIALS ⋮ On Brown polynomials. II ⋮ On the irreducible factors of a polynomial ⋮ Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

Uses Software

• AKIRA

Cites Work

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• A theorem of characterization of residual transcendental extensions of a valuation
• Equivalent forms of Hensel's lemma
• Roots of generalized Schönemann polynomials in Henselian extension fields
• A resultant condition for the irreducibility of the polynomials
• Prolongations of valuations to finite extensions
• On valuations of K(x)
• On a generalization of Eisenstein's irreducibility criterion
• Valued Fields

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