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Differences in sets of lengths of Krull monoids with finite class group

Wolfgang A. Schmid (2005)

Journal de Théorie des Nombres de Bordeaux

Let H be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary p -groups have the same system of sets of lengths if and only if they are isomorphic.

Different groups of circular units of a compositum of real quadratic fields

Radan Kučera (1994)

Acta Arithmetica

There are many different definitions of the group of circular units of a real abelian field. The aim of this paper is to study their relations in the special case of a compositum k of real quadratic fields such that -1 is not a square in the genus field K of k in the narrow sense. The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois...

Differential approach for the study of duals of algebraic-geometric codes on surfaces

Alain Couvreur (2011)

Journal de Théorie des Nombres de Bordeaux

The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code C L ( D , G ) on a curve is the differential code C Ω ( D , G ) . We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples...

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