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Displaying 81 – 100 of 173

Non-existence and splitting theorems for normal integral bases

Cornelius Greither, Henri Johnston (2012)

Annales de l’institut Fourier

We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower $ℚ \subset K \subset L$ forces the tower to be split in a very strong sense.

Nontrivial tame extensions over Hopf orders

Daniel R. Replogle, Robert G. Underwood (2002)

Acta Arithmetica

Normal integral bases and complex conjugation.

Jan Brinkhuis (1987)

Journal für die reine und angewandte Mathematik

Normal Integral Bases and Embedding Problems.

Jan Brinkhuis (1983)

Mathematische Annalen

Normal integral bases and ray class groups

Humio Ichimura (2004)

Acta Arithmetica

Normal integral bases and tameness conditions for Kummer extensions

Ilaria Del Corso, Lorenzo Paolo Rossi (2013)

Acta Arithmetica

We present a detailed analysis of some properties of a general tamely ramified Kummer extension of number fields L/K. Our main achievement is a criterion for the existence of a normal integral basis for a general Kummer extension, which generalizes the existing results. Our approach also allows us to explicitly describe the Steinitz class of L/K and we get an easy criterion for this class to be trivial. In the second part of the paper we restrict to the particular case of tame Kummer extensions...

Normal integral bases and the Spiegelungssatz of Scholz

Jan Brinkhuis (1995)

Acta Arithmetica

Normal integral bases for infinite abelian extensions

Patrik Lundström (2001)

Acta Arithmetica

Note on the Galois module structure of quadratic extensions

Günter Lettl (1994)

Colloquium Mathematicae

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 $ℚ^{(n)} / ℚ^{{(n)}^{+}}$ .

Nouveaux exemples d'extension relatives sans base normale

Jean Cougnard (2001)

Annales de la Faculté des sciences de Toulouse : Mathématiques

On a comparison of Gauss sums with products of Lagrange resolvents

Jan Brinkhuis (1994)

Compositio Mathematica

On a conjecture concerning minus parts in the style of Gross

C. Greither, Radan Kučera (2008)

Acta Arithmetica

On Chinburg's second conjecture for abelian fields.

Cornelius Greither (1996)

Journal für die reine und angewandte Mathematik

On equivariant Dedekind zeta-functions at $s = 1$ .

Breuning, Manuel, Burns, David (2010)

Documenta Mathematica

On finite linear groups stable under Galois operation.

Khrebtova, Ekaterina, Malinin, Dmitry (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On Galois structure of the integers in cyclic extensions of local number fields

G. Griffith Elder (2002)

Journal de théorie des nombres de Bordeaux

Let $p$ be a rational prime, $K$ be a finite extension of the field of $p$ -adic numbers, and let $L / K$ be a totally ramified cyclic extension of degree $p^{n}$ . Restrict the first ramification number of $L / K$ to about half of its possible values, $b_{1} > 1 / 2 \cdot p e_{0} / (p - 1)$ where $e_{0}$ denotes the absolute ramification index of $K$ . Under this loose condition, we explicitly determine the $ℤ_{p} [G]$ -module structure of the ring of integers of $L$ , where $ℤ_{p}$ denotes the $p$ -adic integers and $G$ denotes the Galois group Gal $(L / K)$ . In the process of determining this structure,...

Currently displaying 81 – 100 of 173

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Displaying 81 – 100 of 173

Non-existence and splitting theorems for normal integral bases

Nontrivial tame extensions over Hopf orders

Normal integral bases and complex conjugation.

Normal Integral Bases and Embedding Problems.

Normal integral bases and ray class groups

Normal integral bases and tameness conditions for Kummer extensions

Normal integral bases and the Spiegelungssatz of Scholz

Normal integral bases for infinite abelian extensions

Note on the Galois module structure of quadratic extensions

Nouveaux exemples d'extension relatives sans base normale

On a comparison of Gauss sums with products of Lagrange resolvents

On a conjecture concerning minus parts in the style of Gross

On Chinburg's second conjecture for abelian fields.

On equivariant Dedekind zeta-functions at $s = 1$ .

On finite linear groups stable under Galois operation.

On Galois structure of the integers in cyclic extensions of local number fields

On Hilbert-Speiser type imaginary quadratic fields

On integral normal bases over intermediary fields

On integral Stark conjectures (and multiplicative Galois module structures).

On normal integral bases in ray class fields over imaginary quadratic fields

Currently displaying 81 – 100 of 173