The Hopf Galois Property in Subfield Lattices

Let K/k be a finite separable extension, n its degree and 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 . In...

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Veröffentlicht in:Communications in algebra Jg. 44; H. 1; S. 336 - 353
Hauptverfasser: Crespo, Teresa, Rio, Anna, Vela, Montserrat
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 02.01.2016
Schlagworte:
12 Field theory and polynomials
12F Field extensions
Classificació AMS
Galois theory
Galois, Teoria de
Holomorph
Hopf algebra
Hopf Galois extension
Matemàtiques i estadística
SEPARABLE FIELD-EXTENSIONS
Teoria de nombres
Àlgebra
Àrees temàtiques de la UPC
ISSN:0092-7872, 1532-4125
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Zusammenfassung:Let K/k be a finite separable extension, n its degree and 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 . In this paper we study the case n = 6, and intermediate extensions F/k such that , for degrees n = 4, 5, 6. We present an example of a non almost classically Galois Hopf Galois extension of ℚ 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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2014.982809