A note ON MONOGENEITY of pure number fields

Abstract

Gassert's paper "A NOTE ON THE MONOGENEITY OF POWER MAPS" is cited at least by 17 papers in the context of monogeneity of pure number fields despite some errors that it contains and remarks on it. In this note, we point out some of these errors, and make some improvements on it.

Monogenity and Power Integral Bases: Recent Developments

“…While S. Ahmad, T. Nakahara and M. Syed [1] investigated monogenity of pure sextic fields in 2014 using its subfield structure and relative monogenity, T. A. Gassert [79] already used Montes algorithm in 2017 to describe monogenity of pure fields. Note that it is only about the monogenity of the polynomials and not the monogenity of number fields generated by a root of the polynomial (for some corrections see L. El Fadil [37]).…”

Monogenity and Power Integral Bases: Recent Developments

“…While, in 2014, S. Ahmad, T. Nakahara and M. Syed [21] investigated monogenity properties of pure sextic fields using their subfield structure and relative monogenity, in 2017 T. A. Gassert [22] already used Montes algorithm to describe monogenity of pure fields. Note that this is only about the monogenity of the polynomials and not the monogenity of number fields generated by a root of the polynomial (for some corrections, see L. El Fadil [23]).…”