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Displaying 121 – 140 of 173

PSL $(2, 7)$ septimic fields with a power basis

Melisa J. Lavallee, Blair K. Spearman, Qiduan Yang (2012)

Journal de Théorie des Nombres de Bordeaux

We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group $P S L (2, 7)$ .

Realizable Galois module classes over the group ring for non abelian extensions

Nigel P. Byott, Bouchaïb Sodaïgui (2013)

Annales de l’institut Fourier

Given an algebraic number field $k$ and a finite group $Γ$ , we write $ℛ (O_{k} [Γ])$ for the subset of the locally free classgroup $Cl (O_{k} [Γ])$ consisting of the classes of rings of integers $O_{N}$ in tame Galois extensions $N / k$ with $Gal (N / k) ≅ Γ$ . We determine $ℛ (O_{k} [Γ])$ , and show it is a subgroup of $Cl (O_{k} [Γ])$ by means of a description using a Stickelberger ideal and properties of some cyclic codes, when $k$ contains a root of unity of prime order $p$ and $Γ = V ⋊ C$ , where $V$ is an elementary abelian group of order $p^{r}$ and $C$ is a cyclic group of order $m > 1$ acting faithfully on...

Relative Galois module structure of integers of abelian fields

Nigel P. Byott, Günter Lettl (1996)

Journal de théorie des nombres de Bordeaux

Let $L / K$ be an extension of algebraic number fields, where $L$ is abelian over $ℚ$ . In this paper we give an explicit description of the associated order $𝒜_{L / K}$ of this extension when $K$ is a cyclotomic field, and prove that $o_{L}$ , the ring of integers of $L$ , is then isomorphic to $𝒜_{L / K}$ . This generalizes previous results of Leopoldt, Chan Lim and Bley. Furthermore we show that $𝒜_{L / K}$ is the maximal order if $L / K$ is a cyclic and totally wildly ramified extension which is linearly disjoint to $ℚ^{(m^{'})} / K$ , where $m^{'}$ is the conductor of $K$ .

Relative Galois module structure of rings of integers of cyclomatic fields.

Chong-Hai Lim, Shih-Ping Chan (1993)

Journal für die reine und angewandte Mathematik

Relative integral basis for algebraic number fields.

Haghighi, Mahmood (1986)

International Journal of Mathematics and Mathematical Sciences

Remarks on normal bases

Marcin Mazur (2001)

Colloquium Mathematicae

We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.

Résultats récents sur la monogénéité de certains anneaux d'entiers

J. COUGNARD (1987/1988)

Seminaire de Théorie des Nombres de Bordeaux

Rings of Integers and Trace Forms for Tame Extensions of Odd Degree.

M.J. Taylor (1989)

Mathematische Zeitschrift

Self-dual normal bases for infinite odd abelian Galois ring extensions

Patrik Lundström (2006)

Acta Arithmetica

Signatures of fields and extension theory.

Alex Rosenberg, E. Becker, J. Harman (1982)

Journal für die reine und angewandte Mathematik

Some linear relations between values of trigonometric functions at kπ/n

Kurt Girstmair (1997)

Acta Arithmetica

Some remarks on Hilbert-Speiser and Leopoldt fields of given type

James E. Carter (2007)

Colloquium Mathematicae

Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers $O_{L}$ in L is free as a module over the associated order $_{L / K}$ . We also give examples, some of which show that this result can still hold without the assumption that K contains...

Sommes de Gauss et structure galoisienne des anneaux d'entiers

Jacques QUEYRUT (1981/1982)

Seminaire de Théorie des Nombres de Bordeaux

Splitting fields and group characters.

Richard Anthony Mollin (1980)

Journal für die reine und angewandte Mathematik

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

The Steinitz class of a number field extension $K / k$ is an ideal class in the ring of integers $𝒪_{k}$ of $k$ , which, together with the degree $[K : k]$ of the extension determines the $𝒪_{k}$ -module structure of $𝒪_{K}$ . We denote by $R_{t} (k, G)$ the set of classes which are Steinitz classes of a tamely ramified $G$ -extension of $k$ . We will say that those classes are realizable for the group $G$ ; it is conjectured that the set of realizable classes is always a group.In this paper we will develop some of the ideas contained in [7] to obtain some...

Currently displaying 121 – 140 of 173

Previous Page 7 Next

Displaying 121 – 140 of 173

PSL $(2, 7)$ septimic fields with a power basis

Realizable Galois module classes over the group ring for non abelian extensions

Relative Galois module structure of integers of abelian fields

Relative Galois module structure of rings of integers of cyclomatic fields.

Relative integral basis for algebraic number fields.

Remarks on normal bases

Résultats récents sur la monogénéité de certains anneaux d'entiers

Rings of Integers and Trace Forms for Tame Extensions of Odd Degree.

Self-dual normal bases for infinite odd abelian Galois ring extensions

Signatures of fields and extension theory.

Some linear relations between values of trigonometric functions at kπ/n

Some remarks on Hilbert-Speiser and Leopoldt fields of given type

Sommes de Gauss et structure galoisienne des anneaux d'entiers

Splitting fields and group characters.

Steinitz classes of some abelian and nonabelian extensions of even degree

Steinitz classes of tamely ramified nonabelian extensions of odd prime power order

Structure galoisienne des anneaux d'entiers.

Structure galoisienne des anneaux d'entiers

Structure galoisienne des anneaux d'entiers des extensions de Kummer

Structure galoisienne des anneaux d'entiers d'extensions sauvagement ramifiées

Currently displaying 121 – 140 of 173