INTEGRAL BASES AND MONOGENITY OF PURE NUMBER FIELDS WITH NON-SQUARE FREE PARAMETERS UP TO DEGREE 9

Abstract

Let K be a pure number field generated by a root alpha of a monic irreducible polynomial f(x) = x^n-m with m a rational integer and 3 <= n <= 9 an integer. In this paper, we calculate an integral basis of Z_K, 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 [20] where only square-free values of m were considered.