A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic $p$

Nigel P. Byott

Displaying similar documents to “A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic $p$ ”

PAC fields over number fields

Moshe Jarden (2006)

Journal de Théorie des Nombres de Bordeaux

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We prove that if $K$ is a number field and $N$ is a Galois extension of $ℚ$ which is not algebraically closed, then $N$ is not PAC over $K$ .

Hopf-Galois module structure of tame biquadratic extensions

Paul J. Truman (2012)

Journal de Théorie des Nombres de Bordeaux

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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 $L / K$ with group $G ≅ C_{2} \times C_{2}$ and study in detail the local and global structure of the ring of integers $𝔒_{L}$ as a module over its associated order $𝔄_{H}$ in each of the Hopf algebras $H$ giving a nonclassical Hopf-Galois...

Hopf Galois structures on Kummer extensions of prime power degree.

Childs, Lindsay N. (2011)

The New York Journal of Mathematics [electronic only]

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Automatic realizations of Galois groups with cyclic quotient of order $p^{n}$

Ján Mináč, Andrew Schultz, John Swallow (2008)

Journal de Théorie des Nombres de Bordeaux

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We establish automatic realizations of Galois groups among groups $M ⋊ G$ , where $G$ is a cyclic group of order $p^{n}$ for a prime $p$ and $M$ is a quotient of the group ring $𝔽_{p} [G]$ .

An action-free characterization of weak Hopf-Galois extensions.

Kadison, Lars (2005)

AMA. Algebra Montpellier Announcements [electronic only]

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Note on the Galois module structure of quadratic extensions

Günter Lettl (1994)

Colloquium Mathematicae

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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, $ℚ^{(p)}$ . 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 $ℚ^{(n)} / ℚ^{{(n)}^{+}}$ .

On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.

Chipchakov, Ivan D. (2005)

Acta Universitatis Apulensis. Mathematics - Informatics

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Displaying similar documents to “A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic p ”

PAC fields over number fields

Hopf-Galois module structure of tame biquadratic extensions

Hopf Galois structures on Kummer extensions of prime power degree.

Automatic realizations of Galois groups with cyclic quotient of order p n

An action-free characterization of weak Hopf-Galois extensions.

Note on the Galois module structure of quadratic extensions

On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.

Displaying similar documents to “A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic $p$ ”

Automatic realizations of Galois groups with cyclic quotient of order $p^{n}$