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Proceedings of the American Mathematical Society Series B

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On basic and Bass quaternion orders


Authors: Sara Chari, Daniel Smertnig and John Voight
Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 11-26
DOI: https://doi.org/10.1090/bproc/68
Published electronically: January 13, 2021
MathSciNet review: 4199211
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Abstract | References | Additional Information

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.


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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
Article copyright: © Copyright 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)