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On basic and Bass quaternion orders

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.

preprint2019arXivOpen access
Sara ChariDaniel SmertnigJohn Voight
math.RA
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Sara ChariDaniel SmertnigJohn Voight

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