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Acta Mathematica Vietnamica

On Monogenity of Certain Pure Number Fields Defined by x60m

icon-email Lhoussain El Fadil , Hanan Choulli , Omar Kchit

Abstract

Let K be a pure number field generated by a complex root of a monic irreducible polynomial F(x)=x60mZ[x], with m±1 a square free integer. In this paper, we study the {monogenity} of K. We prove that if m1 (mod 4), m±1 (mod 9) and m{±1,±7} (mod 25), then K is monogenic. But if m1 (mod 4), m±1 (mod 9), or m±1 (mod 25), then K is not monogenic. Our results are illustrated by examples.