AN EXPERIMENT ON THE MONOGENITY OF A FAMILY OF TRINOMIALS

DOI10.17654/NT051010097zbMath1499.11318OpenAlexW3175953741MaRDI QIDQ5074027

István Gaál

Publication date: 6 May 2022

Published in: JP Journal of Algebra, Number Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.17654/nt051010097

zbMATH Keywords

trinomialspower integral basismonogenitysextic fieldsrelative Thue equationscalculating the solutions

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Other number fields (11R21) Computer solution of Diophantine equations (11Y50) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (10)

On non-monogenity of the number fields defined by certain quadrinomials ⋮ Non-monogenity of certain octic number fields defined by trinomials ⋮ On monogenity of certain number fields defined by \(x^8+ax+b\) ⋮ 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 trinomials of type \(x^n +ax^m+b\) ⋮ On common index divisor and monogenity of certain number fields defined by trinomials X⁶ + AX + B ⋮ On index and monogenity of certain number fields defined by trinomials ⋮ On monogenity of certain number fields defined by trinomials ⋮ Common index divisor of the number fields defined by

Uses Software

• Maple

Cites Work

• Computing elements of given index in totally complex cyclic sextic fields
• Power integral bases in a family of sextic fields with quadratic subfields
• The index of a quartic field defined by a trinomial X4 + aX + b
• Infinite families of monogenic trinomials and their Galois groups
• Characterization of primes dividing the index of a trinomial
• Monogenic trinomials with non-squarefree discriminant
• Monogenity in totally complex sextic fields, revisited
• Diophantine Equations and Power Integral Bases
• Calculating “Small” Solutions of Relative Thue Equations

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