English

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

R2 v1 2026-06-23T07:55:57.885Z