On basic and Bass quaternion orders

Sara Chari; Daniel Smertnig; John Voight

doi:10.1090/bproc/68

journal article Open Access Jan 13, 2021

On basic and Bass quaternion orders

Sara Chari Daniel Smertnig

John Voight

Proceedings of the American Mathematical Society, Series B Vol. 8 No. 2 pp. 11-26 · American Mathematical Society (AMS)

View at Publisher Save 10.1090/bproc/68

Abstract

A quaternion order

O

\mathcal {O}

over a Dedekind domain

R
R

is Bass if every

R
R

-superorder is Gorenstein, and

O

\mathcal {O}

is basic if it contains an integrally closed quadratic

R
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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Metrics

6

Citations

17

References

Details

Published: Jan 13, 2021
Vol/Issue: 8(2)
Pages: 11-26
License: View

Authors

Faculty of Mathematics and Physics (FMF), University of Ljubljana and Institute of Mathematics, Physics and Mechanics (IMFM)

J

John Voight

Funding

National Science Foundation Award: J4079-N32

Simons Foundation Award: J4079-N32

Austrian Science Fund Award: J4079-N32

Cite This Article

Sara Chari, Daniel Smertnig, John Voight (2021). On basic and Bass quaternion orders. Proceedings of the American Mathematical Society, Series B, 8(2), 11-26. https://doi.org/10.1090/bproc/68

On basic and Bass quaternion orders

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