On basic and Bass quaternion orders [Elektronski vir]
Chari, Sara ; Smertnig, Daniel ; Voight, John
A quaternion order ▫$\mathcal O$▫ over a Dedekind domain ▫$R$▫ is Bass if every ▫$R$▫-superorder is Gorenstein, and ▫$\mathcal O$▫ 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.
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