On power integral bases of certain pure number fields defined by x^2u⋅3v-m

2021/06/02 by Lhoussain El Fadil, Fadil, Lhoussain El, Ahmed Najim +1
Computer Science · Mathematics · #11R04 #11R16 #11R21 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #G.0 #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2106.01252

openalex publication_date 2021/06/02 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

Abstract

Let K = ℚ (α) be a pure number field generated by a complex root α of a monic irreducible polynomial F(x) = x^{2u⋅ 3v}-m, with m ≠ ± 1 a square free rational integer, u, and v two positive integers. In this paper, we study the monogenity of K. The case u=0 or v=0 has been previously studied. We prove that if m\not≡ 1 (mod4) and m\not≡ ± 1 (mod9), then K is monogenic. But if m≡ 1 (mod4) or m≡ 1 (mod9), then K is not monogenic. Some illustrating examples are given too.

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