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

Kadison, Lars

Displaying similar documents to “An action-free characterization of weak Hopf-Galois extensions.”

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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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...

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

Nigel P. Byott (2011)

Journal de Théorie des Nombres de Bordeaux

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Let $S / R$ be a finite extension of discrete valuation rings of characteristic $p > 0$ , and suppose that the corresponding extension $L / K$ of fields of fractions is separable and is $H$ -Galois for some $K$ -Hopf algebra $H$ . Let $𝔻_{S / R}$ be the different of $S / R$ . We show that if $S / R$ is totally ramified and its degree $n$ is a power of $p$ , then any element $ρ$ of $L$ with $v_{L} (ρ) \equiv - v_{L} (𝔻_{S / R}) - 1 (mod n)$ generates $L$ as an $H$ -module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. G. Elder for Galois...

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 $𝔽_{p} [G]$ .

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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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 $K$ .

Module structure of integers in metacyclic extensions

James Carter (1998)

Colloquium Mathematicae

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Displaying similar documents to “An action-free characterization of weak Hopf-Galois extensions.”

Hopf Galois structures on Kummer extensions of prime power degree.

Hopf-Galois module structure of tame biquadratic extensions

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

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

PAC fields over number fields

Module structure of integers in metacyclic extensions

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

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