On power integral bases for certain pure number fields defined by

Abstract

Let be a pure number field generated by a root α of a monic irreducible polynomial with is a square free integer, r and s are two positive integers. In this article, we study the monogenity of K. We prove that if and then K is monogenic. We give also sufficient conditions on r, s, and m for K to be not monogenic. Some illustrating examples are given too.