Generators for abelian extensions of number fields
Ja Kyung Koo, Dong Hwa Shin

TL;DR
The paper constructs universal primitive generators for abelian extensions of number fields, ensuring their traces generate intermediate fields, and introduces methods for finding normal elements, with applications to ray class fields.
Contribution
It introduces a universal primitive generator construction for abelian extensions and a new method for finding normal elements, advancing explicit generator theory.
Findings
Universal primitive generators can be constructed with trace properties
Applications to towers of ray class fields over imaginary quadratic fields
A new method for finding normal elements in abelian extensions
Abstract
Let be a finite abelian extension of number fields. We first construct a universal primitive generator of over whose relative trace to any intermediate field becomes a generator of over , too. We also develop a similar argument in terms of norm. As its examples we investigate towers of ray class fields over imaginary quadratic fields. And, we further present a new method of finding a normal element for the extension .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Coding theory and cryptography
