Computation of Locally Free Class Groups

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.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: Werner Bley, Robert Boltje
• Keywords: Algorithms, ANTS 2006, Free Class Group, Ray Class Group, Semisimple Algebra