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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Global dimension of orders


Author: Richard B. Tarsy
Journal: Trans. Amer. Math. Soc. 151 (1970), 335-340
MSC: Primary 16.90
MathSciNet review: 0268226
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Abstract: We prove that the finitistic global dimension (fGD) of an order in a quaternion algebra over the quotient field of a Dedekind domain is one. Examples are given of orders of global dimension $ n - 1$ in $ n \times n$ matrices over the quotient field of a discrete valuation ring.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0268226-3
PII: S 0002-9947(1970)0268226-3
Keywords: Global dimension, finitistic global dimension, order, tiled order, discrete valuation ring, regular local ring
Article copyright: © Copyright 1970 American Mathematical Society