On power integral bases for certain pure number fields defined by $x^{18}-m$

. Let K = Q ( α ) be a number field generated by a complex root α of a monic irreducible polynomial f ( x ) = x 18 − m , m 6 = ∓ 1, is a square free rational integer. We prove that if m ≡ 2 or 3 (mod 4) and m 6≡ ∓ 1 (mod 9), then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡ 1 (mod 9), then the number field K is not monogenic.