dc.date.accessioned 2008-02-26T10:53:02Z dc.date.available 2008-02-26T10:53:02Z dc.date.issued 2007 dc.identifier.uri urn:nbn:de:hebis:34-2008022620483 dc.identifier.uri http://hdl.handle.net/123456789/2008022620483 dc.format.extent 274689 bytes dc.format.extent 140309 bytes dc.format.mimetype application/pdf dc.format.mimetype application/pdf dc.language.iso eng dc.subject Galois module structure of rings of integers eng dc.subject associated orders eng dc.subject algebraic number theory computations eng dc.subject.ddc 510 dc.title Computing Generators of Free Modules over Orders in Group Algebras eng dc.type Preprint dcterms.abstract Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ. eng dcterms.accessRights open access dcterms.creator Bley, Werner dcterms.creator Johnston, Henri dcterms.isPartOf Mathematische Schriften Kassel ger dcterms.isPartOf 07, 07 ger dc.subject.msc 11R33 eng dc.subject.msc 11Y40 eng
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