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


Maximal orders over regular local rings

Author: Mark Ramras
Journal: Trans. Amer. Math. Soc. 155 (1971), 345-352
MSC: Primary 16.20
MathSciNet review: 0272808
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Abstract: In this paper various sufficient conditions are given for the maximality of an $ R$-order in a finite-dimensional central simple $ K$-algebra, where $ R$ is a regular local ring whose quotient field is $ K$. Stronger results are obtained when we assume the dimension of $ R$ to be three. This work depends upon earlier results of this author [5] for regular local rings of dimension two, and the fundamental work of Auslander and Goldman [1] for dimension one.

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PII: S 0002-9947(1971)0272808-3
Keywords: Maximal order, central simple algebra, conductor, global dimension, regular local ring, reflexive module
Article copyright: © Copyright 1971 American Mathematical Society