Hopf Galois structures on Kummer extensions of prime power degree.
Childs, Lindsay N. (2011)
The New York Journal of Mathematics [electronic only]
Similarity:
Childs, Lindsay N. (2011)
The New York Journal of Mathematics [electronic only]
Similarity:
Paul J. Truman (2012)
Journal de Théorie des Nombres de Bordeaux
Similarity:
In [] we studied the nonclassical Hopf-Galois module structure of rings of algebraic integers in some tamely ramified extensions of local and global fields, and proved a partial generalisation of Noether’s theorem to this setting. In this paper we consider tame Galois extensions of number fields with group and study in detail the local and global structure of the ring of integers as a module over its associated order in each of the Hopf algebras giving a nonclassical Hopf-Galois...
Nigel P. Byott (2011)
Journal de Théorie des Nombres de Bordeaux
Similarity:
Let be a finite extension of discrete valuation rings of characteristic , and suppose that the corresponding extension of fields of fractions is separable and is -Galois for some -Hopf algebra . Let be the different of . We show that if is totally ramified and its degree is a power of , then any element of with generates as an -module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. G. Elder for Galois...
Moshe Jarden (2006)
Journal de Théorie des Nombres de Bordeaux
Similarity:
We prove that if is a number field and is a Galois extension of which is not algebraically closed, then is not PAC over .
Chipchakov, Ivan D. (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
Similarity:
Kadison, Lars (2005)
AMA. Algebra Montpellier Announcements [electronic only]
Similarity:
Günter Lettl (1994)
Colloquium Mathematicae
Similarity:
In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, . For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of .