On integral bases and monogeneity of pure sextic number fields with non-squarefree coefficients

DOI10.1016/j.jnt.2021.03.025zbMath1479.11182arXiv2202.04417OpenAlexW3160192029WikidataQ114157034 ScholiaQ114157034MaRDI QIDQ2043494

Lhoussain El Fadil

Publication date: 2 August 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.04417

zbMATH Keywords

Newton polygonsindexpower integral basismonogenicDedekind criterionprime ideal factorizationtheorem of Orepure sextic number field

Mathematics Subject Classification ID

Other number fields (11R21) Computer solution of Diophantine equations (11Y50) Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (12)

On monogenity of certain pure number fields defined by $$x^{{2}^{u}.3^{v}} - m$$ ⋮ Nonmonogenity of number fields defined by trinomials ⋮ On common index divisors and monogenity of certain number fields defined by x⁵ + ax² + b ⋮ On non monogenity of certain number fields defined by trinomials \(x^6 + ax^3 + b\) ⋮ On nonmonogenic number fields defined by ⋮ On nonmonogenic algebraic number fields ⋮ On common index divisor and monogenity of certain number fields defined by trinomials X⁶ + AX + B ⋮ ON THE MONOGENITY OF TOTALLY COMPLEX PURE SEXTIC FIELDS ⋮ On monogenity of certain pure number fields defined by \(x^{60} - m\) ⋮ Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9 ⋮ Non-monogenity of some number fields generated by binomials or trinomials of prime-power degree ⋮ On monogenity of certain number fields defined by trinomials

Cites Work

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• Integral bases and monogenity of pure fields
• On a theorem of Ore
• On certain pure sextic fields related to a problem of Hasse
• On the indices of multiquadratic number fields
• NEWTON POLYGONS AND p-INTEGRAL BASES OF QUARTIC NUMBER FIELDS
• Power integral bases for certain pure sextic fields
• Power Integral Bases in Orders of Composite Fields
• Index form equations in sextic fields: a hard computation
• On Newton polygons techniques and factorization of polynomials over Henselian fields
• Newton polygons of higher order in algebraic number theory

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