Computation of locally free class groups

Authors:
Werner Bley;Robert Boltje
Affiliations:
Universität Kassel, Kassel, Germany;University of California, Santa Cruz, CA
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

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Abstract

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.