The Hopf Galois property in subfield lattices
Let K/k be a finite separable extension, n its degree and (K) over tilde /k its Galois closure. For n <= 5, Greither and Pareigis show that all Hopf Galois extensions are either Galois or almost classically Galois and they determine the Hopf Galois character of K/ k according to the Galois group...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2015 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/80143 |
| Acesso em linha: | https://hdl.handle.net/2117/80143 https://dx.doi.org/10.1080/00927872.2014.982809 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Galois theory Holomorph Hopf algebra Hopf Galois extension SEPARABLE FIELD-EXTENSIONS Galois, Teoria de Classificació AMS::12 Field theory and polynomials::12F Field extensions Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Resumo: | Let K/k be a finite separable extension, n its degree and (K) over tilde /k its Galois closure. For n <= 5, Greither and Pareigis show that all Hopf Galois extensions are either Galois or almost classically Galois and they determine the Hopf Galois character of K/ k according to the Galois group (or the degree) of (K) over tilde /k. In this paper we study the case n = 6, and intermediate extensions F/ k such that K subset of F subset of (K) over tilde, for degrees n = 4, 5, 6. We present an example of a non almost classically Galois Hopf Galois extension of (sic) of the smallest possible degree and new examples of Hopf Galois extensions. In the last section we prove a transitivity property of the Hopf Galois condition. |
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