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

Lhoussain El Fadil, Mohamed Faris

• 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.