English

Computing generators of free modules over orders in group algebras II

Number Theory 2010-09-16 v2 Rings and Algebras

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. 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.

Keywords

Cite

@article{arxiv.1006.4381,
  title  = {Computing generators of free modules over orders in group algebras II},
  author = {Werner Bley and Henri Johnston},
  journal= {arXiv preprint arXiv:1006.4381},
  year   = {2010}
}

Comments

26 pages, latex, v2 includes many minor corrections and changes

R2 v1 2026-06-21T15:39:38.543Z