## On basic and Bass quaternion orders

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Sara Chari, Daniel Smertnig and John Voight
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**8**(2021), 11-26

## Abstract:

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.## References

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## Additional Information

**Sara Chari**- Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
- MR Author ID: 1341376
- Email: schari0301@gmail.com
**Daniel Smertnig**- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
- MR Author ID: 916775
- Email: dsmertni@uwaterloo.ca
**John Voight**- Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
- MR Author ID: 727424
- ORCID: 0000-0001-7494-8732
- Email: jvoight@gmail.com
- Received by editor(s): March 14, 2019
- Received by editor(s) in revised form: October 31, 2020
- Published electronically: January 13, 2021
- Additional Notes: The second author was supported by the Austrian Science Fund (FWF) project J4079-N32.

The third author was supported by an NSF CAREER Award (DMS-1151047) and a Simons Collaboration Grant (550029). - Communicated by: Benjamin Brubaker
- © Copyright 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B
**8**(2021), 11-26 - DOI: https://doi.org/10.1090/bproc/68
- MathSciNet review: 4199211