On power integral bases of certain pure number fields defined by X84 − m

Lhoussain El Fadil ^[1] ; Mohamed Faris ^[1]
1. [1] University of Sidi Mohamed Ben Abdellah, Marruecos
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 65, Nº. 1, 2023, págs. 197-211
Idioma: inglés
DOI: 10.33044/revuma.2836
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Resumen
- Let K = Q(α) be a pure number field generated by a complex root α of a monic irreducible polynomial F(x) = x 84 − m, with m ̸= ±1 a square-free integer. In this paper, we study the monogeneity of K. We prove that if m ̸≡ 1 (mod 4), m ̸≡ ±1 (mod 9), and m ̸∈ {±1, ±18, ±19} (mod 49), then K is monogenic. But if m ≡ 1 (mod 4) or m ≡ ±1 (mod 9) or m ≡ 1 (mod 49), then K is not monogenic. Some illustrating examples are given.