Ideal classes of orders in quaternion algebras

Abstract

We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right $O$-ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.

arXiv commentaccepted version, with an appendix by John Voight

References in corpus (6)

• Computing the ideal class monoid of an order
• Computing square-free polarized abelian varieties over finite fields
• Almost ordinary abelian varieties over finite fields
• Computing ideal classes representatives in quaternion algebras
• Definite orders with locally free cancellation
• An algorithm for the principal ideal problem in indefinite quaternion algebras