On power integral bases of certain pure number fields defined by x3r-m

Let K = Q ( α ) be a pure number field generated by a root α of a monic irreducible polynomial F ( x ) = x 3 r - m , with m ≠ ± 1 is a square-free rational integer and r is a positive integer. In this paper, we study the monogenity of K . We prove that if m ≢ ± 1 (mod 9 ) , then K is monogenic. We give also sufficient conditions on r and m for K to be not monogenic. Some illustrating examples are given too.