PSL septimic fields with a power basis
We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group .
Realizable Galois module classes over the group ring for non abelian extensions
Given an algebraic number field and a finite group , we write for the subset of the locally free classgroup consisting of the classes of rings of integers in tame Galois extensions with . We determine , and show it is a subgroup of by means of a description using a Stickelberger ideal and properties of some cyclic codes, when contains a root of unity of prime order and , where is an elementary abelian group of order and is a cyclic group of order acting faithfully on...
Relative Galois module structure of integers of abelian fields
Let be an extension of algebraic number fields, where is abelian over . In this paper we give an explicit description of the associated order of this extension when is a cyclotomic field, and prove that , the ring of integers of , is then isomorphic to . This generalizes previous results of Leopoldt, Chan Lim and Bley. Furthermore we show that is the maximal order if is a cyclic and totally wildly ramified extension which is linearly disjoint to , where is the conductor of .
Relative Galois module structure of rings of integers of cyclomatic fields.
Relative integral basis for algebraic number fields.
Remarks on normal bases
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
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
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 in L is free as a module over the associated order . 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
Splitting fields and group characters.
Steinitz classes of some abelian and nonabelian extensions of even degree
The Steinitz class of a number field extension is an ideal class in the ring of integers of , which, together with the degree of the extension determines the -module structure of . We denote by the set of classes which are Steinitz classes of a tamely ramified -extension of . We will say that those classes are realizable for the group ; 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...
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