Combinatorics

Discrete mathematics

Dedekind sum

Factorization

Pure mathematics

Ideal (ethics)

Mathematics

Algorithm

Mathematical proof

Epistemology

Algebraic number field

Square (algebra)

Philosophy

Prime power

Prime (order theory)

Square-free integer

Programming language

Geometry

Computer science

Dedekind cut

Field (mathematics)

Integer (computer science)

Boletim da Sociedade Paranaense de Matemática

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.

On power integral bases for certain pure sextic fields