2024/06/30 by Hamid Ben Yakkou, Brahim Boudine, Yakkou, Hamid Ben +2
Mathematics · #11A63 #11R04 #11R16 #11R21 #11Y40 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #F.2.2 #FOS: Mathematics #History and Theory of Mathematics #Mathematics #Number Theory (math.NT) #Physics #Statistical physics
paper · pdf · doi:10.48550/arxiv.2407.00819
openalex publication_date 2024/06/30 · openalex created_date 2024/07/06 · openalex updated_date 2026/08/06
Let m be a rational integer with m ≠ 0, ± 1, and consider the pure number field K = ℚ(√[n]m) with n ≥ 3. Most papers discussing the monogenity of pure number fields focus exclusively on the case where m is square-free. For every integer n ≥ 4, the monogenity of number fields of degree n is not completely characterized. For example, the monogenity of the pure quartic field ℚ(√[4]m) is not yet fully described, even when m is square-free (see the recent 2024 paper \citeNyul by Arnóczki and Nyul). In this paper, based on a classical theorem of Ore concerning prime ideal decomposition in number fields \citeMN92, O, we study the monogenity of K without assuming m to be square-free. As an application, we present several examples related to canonical number systems (CNS). In particular, we observe that our results extend some of those presented in \citeBFC, BF, HNHCNS.