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arXiv · 1903.00560

On basic and Bass quaternion orders

Sara Chari·Daniel Smertnig·John Voight
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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.

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Sara Chari, Daniel Smertnig, John Voight. 2019-03-01. On basic and Bass quaternion orders. https://doi.org/10.1090/bproc%2F68

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