On basic and Bass quaternion orders
Rings and Algebras
2026-01-13 v1
Abstract
A quaternion order O over a Dedekind domain R is Bass if every R-superorder is Gorenstein, and O is basic if it contains an integrally closed quadratic R-order. In this article, we show that these conditions are equivalent in local and global settings: a quaternion order is Bass if and only if it is basic. In particular, we show that the property of being basic is a local property of a quaternion order.
Cite
@article{arxiv.1903.00560,
title = {On basic and Bass quaternion orders},
author = {Sara Chari and Daniel Smertnig and John Voight},
journal= {arXiv preprint arXiv:1903.00560},
year = {2026}
}
Comments
15 pages