Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials

TL;DR

This paper characterizes all generators of power integral bases in certain quartic fields defined by monogenic polynomials, expanding understanding of their algebraic structure and monogenicity.

Contribution

It provides a complete description of power integral bases in quartic fields associated with specific monogenic polynomial families, building on prior classifications.

Findings

All generators of power integral bases are described for the considered fields.

The paper extends previous classifications of monogenic quartic fields.

Results contribute to the understanding of algebraic integers in these fields.

Abstract

J. Harrington and L. Jones characterized monogenity of four new parametric families of quartic polynomials with various Galois groups. A short time later P. Voutier added a cyclic family. In this note we intend to describe all generators of power integral bases in the number fields generated by a root of the monogenic polynomials.