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

2024/05/22 by Gaál, István
#11D25 #11R04 #11Y50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2405.13429

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.

Related

• Power integral bases in a family of octic fields
• Two Families of Monogenic S₄ Quartic Number Fields
• A family of cyclic quartic monogenic polynomials
• On the monogenity of quartic number fields defined by x⁴+ax²+b
• Monogenic Reciprocal Quartic Polynomials And Their Galois Groups