2010/06/22 by Werner Bley, Bley, Werner, Henri Johnston +1
Mathematics · #11R33 #11Y40 #16Z05 #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11R33 #msc:11Y40 #msc:16Z05
paper · pdf · doi:10.48550/arxiv.1006.4381
26 pages, latex, v2 includes many minor corrections and changes
arxiv created 2010/09/15 · arxiv updated 2010/09/16
Let E be a number field and G be a finite group. Let A be any OE-order of full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous article, we gave a necessary and sufficient condition for X to be free of given rank d over A. In the case that (i) the Wedderburn decomposition of E[G] is explicitly computable and (ii) each component is in fact a matrix ring over a field, this led to an algorithm that either gives elements that either gives an A-basis for X or determines that no such basis exists. In the present article, we generalise the algorithm by weakening condition (ii) considerably.