On monogenity of certain pure number fields defined by x^pr-m

2021/02/03 by Hamid Ben Yakkou, Yakkou, Hamid Ben, Lhoussain El Fadil +1
Mathematics · #11R04 #11R16 #11R21 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2102.01967

openalex publication_date 2021/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K = ℚ (α) be a pure number field generated by a complex root α a monic irreducible polynomial F(x) = x^pr -m, with m ≠ 1 is a square free rational integer, p is a rational prime integer, and r is a positive integer. In this paper, we study the monogenity of K. We prove that if ν_p(m^p-m)=1, then K is monogenic. But if r≥ p and ν_p(m^p-m)> p, then K is not monogenic. Some illustrating examples are given.

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