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dc.rightsUrheberrechtlich geschützt
dc.subjectGalois module structure of rings of integerseng
dc.subjectassociated orderseng
dc.subjectalgebraic number theory computationseng
dc.titleComputing Generators of Free Modules over Orders in Group Algebraseng
dcterms.abstractLet 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.accessRightsopen access
dcterms.creatorBley, Werner
dcterms.creatorJohnston, Henri
dcterms.isPartOfMathematische Schriften Kassel ;; 07, 07ger
dcterms.source.journalMathematische Schriften Kasselger
dcterms.source.volume07, 07

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