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Anneaux d’entiers stablement libres sur [ H 8 × C 2 ]

Jean Cougnard (1998)

Journal de théorie des nombres de Bordeaux

Le groupe H 8 × C 2 est le plus petit groupe pour lequel existent des modules stablement libres non libres. On montre que toutes les classes d’isomorphisme de tels modules peuvent être représentées une infinité de fois par des anneaux d’entiers. On applique un travail de classification de Swan, pour cela on doit construire explicitement des bases normales d’entiers d’extensions à groupe H 8 ; cela se fait en liant un critère de Martinet avec une construction de Witt.

Galois module structure of generalized jacobians.

G. D. Villa-Salvador, M. Rzedowski-Calderón (1997)

Revista Matemática de la Universidad Complutense de Madrid

For a prime number l and for a finite Galois l-extension of function fields L / K over an algebraically closed field of characteristic p <> l, it is obtained the Galois module structure of the generalized Jacobian associated to L, l and the ramified prime divisors. In the cyclic case an implicit integral representation of the Jacobian is obtained and this representation is compared with the explicit representation.

Galois module structure of the rings of integers in wildly ramified extensions

Stephen M. J. Wilson (1989)

Annales de l'institut Fourier

The main results of this paper may be loosely stated as follows.Theorem.— Let N and N ' be sums of Galois algebras with group Γ over algebraic number fields. Suppose that N and N ' have the same dimension and that they are identical at their wildly ramified primes. Then (writing 𝒪 N for the maximal order in N ) 𝒪 N 𝒪 N Γ Γ 𝒪 N ' 𝒪 N ' Γ . In many cases 𝒪 N Γ 𝒪 N ' . The role played by the root numbers of N and N ' at the symplectic characters of Γ in determining the relationship between the Γ -modules 𝒪 N and 𝒪 N ' is described. The theorem includes...

Hereditary orders

Irving Reiner (1974)

Rendiconti del Seminario Matematico della Università di Padova

Holonomy groups of flat manifolds with the R property

Rafał Lutowski, Andrzej Szczepański (2013)

Fundamenta Mathematicae

Let M be a flat manifold. We say that M has the R property if the Reidemeister number R(f) is infinite for every homeomorphism f: M → M. We investigate relations between the holonomy representation ρ of M and the R property. When the holonomy group of M is solvable we show that if ρ has a unique ℝ-irreducible subrepresentation of odd degree then M has the R property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].

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