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Let be an abelian extension of -adic fields, and let denote the valuation ring of . We study ideals of the valuation ring of as integral representations of the Galois group . Assuming is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an -order in the group algebra . We obtain several general and also explicit new results.
On démontre ici un lemme de Hensel pour les opérateurs différentiels. On en déduit un
théorème de factorisation pour des opérateurs différentiels à coefficients dans une
extension liouvillienne transcendante d’un corps valué. On obtient en particulier un
théorème de factorisation pour des opérateurs différentiels à coefficients dans une
extension de par un nombre fini d’exponentielles et de logarithmes
algébriquement indépendants sur .
Let H be a Krull monoid with infinite class group and such that each divisor class of H contains a prime divisor. We show that for each finite set L of integers ≥2 there exists some h ∈ H such that the following are equivalent: (i) h has a representation for some irreducible elements , (ii) k ∈ L.
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