Some explicit constructions of integral structures in quaternion algebras

Abstract

Let B be an undefined quaternion algebra over Q. Following the explicit chacterization of some Eichler orders in B given by Hashimoto, we define explicit embeddings of these orders in some local rings of matrices; we describe the two natural inclusions of an Eichler order of leven Nq in an Eichler order of level N. Moreover we provide a basis for a chain of Eichler orders in B and prove results about their intersection.