A note ON MONOGENEITY of pure number fields

TL;DR

This paper revisits Gassert's work on the monogeneity of pure number fields, identifies errors, and offers improvements to clarify the conditions under which these fields are monogenic.

Contribution

It corrects and refines previous results on the monogeneity of pure number fields, providing clearer criteria and addressing errors in earlier work.

Findings

Identified errors in Gassert's original paper

Provided corrected conditions for monogeneity

Enhanced understanding of pure number field structures

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.