On power integral bases of certain pure number fields defined by X⁶⁰-m

2021/11/10 by Lhoussain El Fadil, Fadil, Lhoussain El, Omar Kchit +3
Mathematics · #11R04 #11R21 #11Y40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #C.m #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.05899

openalex publication_date 2021/11/10 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Let K be a pure number field generated by a complex root of a monic irreducible polynomial F(x)=x⁶⁰-m∈ ℤ[x], with m≠ ±1 a square free integer. In this paper, we study the monogeneity of K. We prove that if m\not≡ 1\md4, m\not≡ ∓ 1 \md9 and m\not∈\∓ 1,∓ 7\ \md25, then K is monogenic. But if m≡ 1\md4, m≡ ∓1 \md9, or m≡ ∓ 1\md25, then K is not monogenic. Our results are illustrated by examples.

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