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G L n -Invariant tensors and graphs

Martin Markl (2008)

Archivum Mathematicum

We describe a correspondence between GL n -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.

G -nilpotent units of commutative group rings

Peter Vassilev Danchev (2012)

Commentationes Mathematicae Universitatis Carolinae

Suppose R is a commutative unital ring and G is an abelian group. We give a general criterion only in terms of R and G when all normalized units in the commutative group ring R G are G -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].

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 ideals in wildly ramified cyclic extensions of degree p 2

Gove Griffith Elder (1995)

Annales de l'institut Fourier

For L / K , any totally ramified cyclic extension of degree p 2 of local fields which are finite extensions of the field of p -adic numbers, we describe the p [ Gal ( L / K ) ] -module structure of each fractional ideal of L explicitly in terms of the 4 p + 1 indecomposable p [ Gal ( L / K ) ] -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

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...

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