Genus fields of Kummer ℓn-cyclic extensions
| Autor: | Gabriel Villa-Salvador, Carlos Daniel Reyes-Morales |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics::Number Theory Computer Science::Information Retrieval General Mathematics Astrophysics::Instrumentation and Methods for Astrophysics Prime number Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Field (mathematics) Function (mathematics) Genus (mathematics) Computer Science::General Literature Congruence (manifolds) Genus field Mathematics |
| Zdroj: | International Journal of Mathematics. 32:2150062 |
| ISSN: | 1793-6519 0129-167X |
| Popis: | We give a construction of the genus field for Kummer [Formula: see text]-cyclic extensions of rational congruence function fields, where [Formula: see text] is a prime number. First, we compute the genus field of a field contained in a cyclotomic function field, and then for the general case. This generalizes the result obtained by Peng for a Kummer [Formula: see text]-cyclic extension. Finally, we study the extension [Formula: see text], for [Formula: see text], [Formula: see text] abelian extensions of [Formula: see text]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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