On the monogenity of quartic number fields defined by x⁴+ax²+b

2022/04/07 by Lhoussain El Fadil, Fadil, Lhoussain El, István Gaál +1
Mathematics · #11R04 #11R09 #11R21 #11Y40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2204.03226

openalex publication_date 2022/04/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

For any quartic number field K generated by a root α of an irreducible trinomial of type x⁴+ax²+b∈ Z[x], we characterize when Z[α] is integrally closed. Also for p=2,3, we explicitly give the highest power of p dividing i(K), the common index divisor of K. For a wide class of monogenic trinomials of this type we prove that up to equivalence there is only one generator of power integral bases in K=Q(α). We illustrate our statements with a series of examples.

Related

• On indices and monogenity of quartic number fields defined by quadrinomials
• On monogenity of certain number fields defined by trinomials
• Two Families of Monogenic S₄ Quartic Number Fields
• On index divisors and monogenity of certain number fields defined by trinomials
• Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials