Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields

TL;DR

This paper presents an efficient algorithm for determining generators of power integral bases in composites of totally real and imaginary quadratic fields, with applications to monogenity in specific quartic fields.

Contribution

The authors develop a new algorithm that reduces the problem to solving index form equations, enabling analysis of monogenity in complex field extensions.

Findings

Algorithm successfully computes generators in composite fields

Monogenity is characterized in the family of imaginary quadratic extensions of simplest quartic fields

Method simplifies the analysis of power integral bases in complex field structures

Abstract

We describe an efficient algorithm to calculate generators of power integral bases in composites of totally real fields with imaginary quadratic fields. We show that the calculation can be reduced to solving index form equations in the original totally real fields. We illustrate our method by investigating monogenity in the infinite parametric family of imaginary quadratic extensions of the simplest quartic fields.