Computing generators of free modules over orders in group algebras
| dc.creator | Bley, Werner | |
| dc.creator | Johnston, Henri | |
| dc.date | 2007-10-31 | |
| dc.date | 2008-01-28 | |
| dc.date.accessioned | 2026-07-07T08:56:23Z | |
| dc.date.available | 2026-07-07T08:56:23Z | |
| dc.description | 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 of E[G] is explicitly computable and each component is in fact a matrix ring over a field, this leads to an algorithm that either gives an A-basis for X or determines that no such basis exists. 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 of O_L in E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K=E=Q. | |
| dc.description | 17 pages, latex, minor revisions | |
| dc.identifier | https://arxiv.org/abs/0710.5869 | |
| dc.identifier | http://arxiv.org/abs/0710.5869 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146589 | |
| dc.subject | Number Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 11R33, 11Y40, 16Z05 | |
| dc.title | Computing generators of free modules over orders in group algebras | |
| dc.type | text |