Explicit construction of integral bases of radical function fields
type: Item
instance of: scholarly article
title: Explicit construction of integral bases of radical function fields
zbMATH Open document ID: 1236.11089
author: Qingquan Wu
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2011-01-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116399
review text: The author determines explicit formulae for integral bases of radical extensions \(K\) of degree \(n\) over global rational function fields. He stipulates that the characteristic of the field of constants does not divide \(n\) thus avoiding wild ramification. Under that assumption he easily deduces an explicit formula for the discriminant of \(K\). Then he presents a suitable basis of \(K\) and proves by combinatorial means that it has the correct discriminant and is therefore an integral basis. In the last section he discusses the decomposition of primes in \(K\) and gives formulae for their degrees of inertia and their ramification indices.
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11Y40
zbMATH DE Number: 5831872
zbMATH Keywords: integral bases
zbMATH Keywords: radical function fields
reviewed by: Michael E. Pohst
describes a project that uses: Magma
MaRDI profile type: Publication
OpenAlex ID: W2329847744
cites work: The Magma algebra system. I: The user language
cites work: Approximating rings of integers in number fields
cites work: Q3139838
cites work: Q5830705
cites work: Integral bases for quartic fields with quadratic subfields
cites work: The integers of a cyclic quartic field
cites work: Q4044675
cites work: Q3999066
cites work: Ramification indices, differents, and integral bases for radical extensions. I.
cites work: Q4429278
cites work: On Integral Bases
cites work: Prime ideal decomposition in \(F({\root m\of\mu})\)
cites work: Number fields
cites work: Integral Bases in Kummer Extensions of Dedekind Fields
cites work: Structure theorems for radical extensions of fields
cites work: Integral basis of the field \(\mathbb Q(\root n\of a)\)
cites work: Q4692759
cites work: Q5659654
cites work: Q2776773
cites work: Voronoi's algorithm in purely cubic congruence function fields of unit rank 1
cites work: Algebraic function fields and codes
cites work: An algorithm for computing an integral basis in an algebraic function field
cites work: Prime ideal decomposition in \(F(\mu^{1/p})\)
cites work: A polynomial-time complexity bound for the computation of the singular part of a Puiseux expansion of an algebraic function
DOI: 10.5802/JTNB.714
description: scientific article; zbMATH DE number 5831872