Relative power integral bases in infinite families of quartic extensions of quadratic fields
Istv\'an Ga\'al, T\'i mea Szab\'o
TL;DR
This paper investigates infinite families of octic fields that are quartic extensions of quadratic fields, focusing on describing all relative power integral bases within these fields.
Contribution
It provides a complete description of all relative power integral bases in infinite parametric families of octic fields over quadratic subfields.
Findings
All relative power integral bases are characterized for the families studied.
The structure of these bases is explicitly described.
The results extend understanding of integral bases in complex field extensions.
Abstract
We consider infinite parametric families of octic fields, that are quartic extensions of quadratic fields. We describe all relative power integral bases of the octic fields over the quadratic subfields.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Finite Group Theory Research