On power integral bases for certain pure sextic fields
Abstract
In their paper [1], Shahzad Ahmad et al. given a characterization on any pure sextic number field Q(m1/6) with square-free integers m satisfying m 6 ±1 (mod 9) to have a power integral bases or do not. In this paper, for these results, we give a new easier proof than that given in [1]. We further investigate the cases m 1 (mod 4) independently to the satisfaction of m2 1 (mod 9), m 1 (mod 9), and the number fields defined by x2r3t
−m, where r, t are two non-negative integers, and m is a square free integer are investigated. The proposed proofs are based on Dedekind’s criterion and on prime ideal factorization.
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References
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