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

2021/02/28 by István Gaál, Gaál, István · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Nonlinear Waves and Solitons #math.NT #msc:11R04 #msc:11R16

paper · pdf · doi:10.48550/arxiv.2103.00444

arxiv created 2021/02/28 · arxiv updated 2021/03/02

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.

Cited by

• Investigating monogenity in a family of cyclic sextic fields

Related

• Integral bases and monogenity of composite fields
• Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials
• On the monogenity of totally complex pure octic fields
• On the monogenity of quartic number fields defined by x⁴+ax²+b
• Exceptional Quartics are Ubiquitous