Výsledky vyhledávání - "12 Field theory and polynomials::12F Field extensions [Classificació AMS]"

Inducing braces and Hopf Galois structures

Autor: Teresa Crespo, Daniel Gil-Muñoz, Anna Rio, Montserrat Vela

Let $p$ be a prime number and let $n$ be an integer not divisible by $p$ and such that every group of order $np$ has a normal subgroup of order $p$. (This holds in particular for $p>n$.) We prove that left braces of size $np$ may be obtained as a sem

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb8378d631c5cf0610c714c862f1e4d4
http://arxiv.org/abs/2206.03810

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Induced Hopf Galois structures and their local Hopf Galois modules

Autor: Daniel Gil Muñoz, Anna Rio

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

The regular subgroup determining an induced Hopf Galois structure for a Galois extension $L/K$ is obtained as the direct product of the corresponding regular groups of the inducing subextensions. We describe here the associated Hopf algebra and Hopf

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a084117658c27b0b523b9933c941460
https://hdl.handle.net/2117/366323

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Revisiting Kneser’s Theorem for Field Extensions

Autor: Gilles Zémor, Christine Bachoc, Oriol Serra

Publikováno v: Combinatorica
Combinatorica, Springer Verlag, 2018, 38 (4), pp.759-777
Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an altern

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6092aae023863e31b393aeb69987d9f
https://hal.archives-ouvertes.fr/hal-01951358

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Hopf Galois structures on symmetric and alternating extensions

Autor: Crespo, T., Rio, A., Montserrat Vela

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Scopus-Elsevier
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

By using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois extensions with Galois group isomorphic to alternating or symmetric groups. Our theory of induce

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0af78b0a08bdcdc822563f185e49221d
http://arxiv.org/abs/1703.02600

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Induced Hopf Galois structures

Autor: Ana Río Doval, Maria Montserrat Vela del Olmo, Teresa Crespo Vicente

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

For a ¿nite Galois extension K/k and an intermediate ¿eld F such that Gal(K/F)has a normal complement in Gal(K/k), we construct and characterize Hopf Galois structures on K/k which are induced by a pair of Hopf Galois structures on K/F and F/k.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8aea553620c846c96bcdff22a9d92190
http://hdl.handle.net/2117/99988

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On the Galois correspondence theorem in separable Hopf Galois theory

Autor: Crespo, Teresa, Rio, Anna, Vela, Montserrat

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Publ. Mat. 60, no. 1 (2016), 221-234
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Dipòsit Digital de la UB
Universidad de Barcelona
Publicacions Matemàtiques; Vol. 60, Núm. 1 (2016); p. 221-234

In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ac7cf466d6776a41a620744c8c147119
http://arxiv.org/abs/1405.0881

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The Hopf Galois property in subfield lattices

Autor: Anna Rio, Teresa Crespo, Montserrat Vela

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

Let K/k be a finite separable extension, n its degree and (K) over tilde /k its Galois closure. For n

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6f28074971fd5b3599d67f0aae6c9fe9
http://arxiv.org/abs/1309.5754

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From Galois to Hopf Galois: theory and practice

Autor: Ana Río Doval, Teresa Crespo Vicente, Maria Montserrat Vela del Olmo

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Hopf Galois theory expands the classical Galois theory by con- sidering the Galois property in terms of the action of the group algebra k [ G ] on K/k and then replacing it by the action of a Hopf algebra. We review the case of separable extensions w

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6c506d712e098e36be445132c28d2b2
http://hdl.handle.net/2117/80188

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Generic Galois extensions for SL_2(F_5) over Q

Autor: Plans Berenguer, Bernat

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of characteristic $0$, we prove

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::1421ab7caeae71fbc1f95d8c890090de
http://hdl.handle.net/2117/1955

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On Noether's rationality problem for cyclic groups over Q

Autor: Plans Berenguer, Bernat|||0000-0003-2718-3436

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Let p be a prime number. Let C p , the cyclic group of order p , permute transitively a set of indeterminates f x 1 ;:::;x p g . We prove that the invariant eld Q ( x 1 ;:::;x p ) C p is rational over Q if and only if the ( p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::cd4693ae4411416b7743b7635602af6a
http://hdl.handle.net/2117/104804

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