Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

Abstract

Abstract Let K be a pure number field generated by a root α of a monic irreducible polynomial f (x)= xn − m with m a rational integer and 3 ≤ n ≤ 9 an integer. In this paper, we calculate an integral basis of ℤK , and we study the monogenity of K, extending former results to the case when m is not necessarily square-free. Collecting and completing the corresponding results in this more general case, our purpose is to provide a parallel to [Gaál, I.—Remete, L.: Power integral bases and monogenity of pure fields,J.Number Theory, 173 (2017), 129–146], where only square-free values of m were considered.