It is advantageous for the study
of the spinor genus of quaternion orders to realize each order as corresponding to a
ternary lattice. In the two known correspondences, those of Eichler and Pall, the
question of whether the mapping is onto or not is not considered. Peters has
investigated the question for Eichler’s correspondence, and his results show that it
is not onto. Pall’s correspondence, though onto, is only defined over the
rational integers. In this article, a generalization to Dedekind domains of Pall’s
correspondence is defined. Those orders which are images of ternary lattices under
the correspondence are completely determined, and the relationship of this mapping
to Eichler’s is examined.
