On basic and Bass quaternion orders

Chari, Sara; Smertnig, Daniel; Voight, John

doi:10.1090/bproc/68

On basic and Bass quaternion orders
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by Sara Chari, Daniel Smertnig and John Voight;

Proc. Amer. Math. Soc. Ser. B 8 (2021), 11-26

DOI: https://doi.org/10.1090/bproc/68

Published electronically: January 13, 2021

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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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Bibliographic 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
Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 11-26
DOI: https://doi.org/10.1090/bproc/68
MathSciNet review: 4199211