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The Hopf Galois property in subfield lattices
dc.contributor.author | Crespo Vicente, Teresa |
dc.contributor.author | Río Doval, Ana |
dc.contributor.author | Vela del Olmo, Maria Montserrat |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2015-12-03T09:52:31Z |
dc.date.available | 2017-01-31T01:30:41Z |
dc.date.issued | 2016-01-01 |
dc.identifier.citation | Crespo, T., Rio, A., Vela, M. The Hopf Galois property in subfield lattices. "Communications in algebra", 01 Gener 2016, vol. 44, núm. 1, p. 336-353. |
dc.identifier.issn | 0092-7872 |
dc.identifier.uri | http://hdl.handle.net/2117/80143 |
dc.description.abstract | 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. |
dc.format.extent | 18 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
dc.subject.lcsh | Galois theory |
dc.subject.other | Holomorph |
dc.subject.other | Hopf algebra |
dc.subject.other | Hopf Galois extension |
dc.subject.other | SEPARABLE FIELD-EXTENSIONS |
dc.title | The Hopf Galois property in subfield lattices |
dc.type | Article |
dc.subject.lemac | Galois, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
dc.identifier.doi | 10.1080/00927872.2014.982809 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::12 Field theory and polynomials::12F Field extensions |
dc.rights.access | Open Access |
local.identifier.drac | 17229732 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/ES/1PE/MTM2012-34611 |
local.citation.author | Crespo, T.; Rio, A.; Vela, M. |
local.citation.publicationName | Communications in algebra |
local.citation.volume | 44 |
local.citation.number | 1 |
local.citation.startingPage | 336 |
local.citation.endingPage | 353 |
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