Computing Generators of Free Modules over Orders in Group Algebras
| 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.rights | Urheberrechtlich geschützt | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| 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 ;; 07, 07 | ger |
| dc.subject.msc | 11R33 | eng |
| dc.subject.msc | 11Y40 | eng |
| dcterms.source.journal | Mathematische Schriften Kassel | ger |
| dcterms.source.volume | 07, 07 |
