A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields

We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a global rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in general.

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Main Authors: Martha Rzedowski-Calderón, Gabriel Villa-Salvador
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/13/11/734
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author Martha Rzedowski-Calderón
Gabriel Villa-Salvador
author_facet Martha Rzedowski-Calderón
Gabriel Villa-Salvador
author_sort Martha Rzedowski-Calderón
collection DOAJ
description We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a global rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in general.
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institution OA Journals
issn 2075-1680
language English
publishDate 2024-10-01
publisher MDPI AG
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series Axioms
spelling doaj-art-7e51ecf208fd4d97938cbe7ae4942be02025-08-20T02:08:08ZengMDPI AGAxioms2075-16802024-10-01131173410.3390/axioms13110734A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function FieldsMartha Rzedowski-Calderón0Gabriel Villa-Salvador1Departamento de Control Automático, Centro de Investigación de Estudios Avanzados del I.P.N., Mexico City 07340, MexicoDepartamento de Control Automático, Centro de Investigación de Estudios Avanzados del I.P.N., Mexico City 07340, MexicoWe consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a global rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in general.https://www.mdpi.com/2075-1680/13/11/734global fieldsextended genus fieldsKummer extensions
spellingShingle Martha Rzedowski-Calderón
Gabriel Villa-Salvador
A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields
Axioms
global fields
extended genus fields
Kummer extensions
title A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields
title_full A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields
title_fullStr A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields
title_full_unstemmed A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields
title_short A Note on Extended Genus Fields of Kummer Extensions of Global Rational Function Fields
title_sort note on extended genus fields of kummer extensions of global rational function fields
topic global fields
extended genus fields
Kummer extensions
url https://www.mdpi.com/2075-1680/13/11/734
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