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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| Language: | English |
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MDPI AG
2024-10-01
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| Series: | Axioms |
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| 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. |
| format | Article |
| id | doaj-art-7e51ecf208fd4d97938cbe7ae4942be0 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| 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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