On power integral bases for certain pure number fields defined by x2r.5s−m

On power integral bases for certain pure number fields defined by $x^{2\cdot 3^k}-m$

“…In particular, for any side S of N , we have f S (y) = f S (y). Lemma 3.7 (see [3]). Let p be a rational prime integer and r a positive integer.…”

“…In [20], by applying the explicit form of index, Gaál and Remete obtained new results on monogeneity of number fields generated by m 1/n , where 3 ≤ n ≤ 9. In 2020, based on Newton polygon techniques, we studied the monogeneity of some pure number fields [8,11,12,9,10,4,3].…”

On power integral bases of certain pure number fields defined by $$x^{42} - m$$

“…While Gaa ´l's and Remete's techniques are based on the index calculation and Nakahara's methods are based on the existence of power relative integral bases of some special sub-fields, the goal of this paper is to study the monogenity of pure number fields K ¼ QðaÞ generated by a complex root a of a monic irreducible polynomial FðxÞ ¼ x 42 À m, where m 6 ¼ AE1 is a square-free rational integer. As in [3][4][5][7][8][9], our method is based on prime ideal factorization.…”