Orders in separable algebras
Abstract: The module , where is an order in a separable algebra over the quotient field of an integrally closed, quasi-local domain, is studied. It is shown that if the domain is complete, contains one element from each isomorphism class of irreducible modules. Also, in general, if the global dimension of is finite, then it equals the homological dimension of .
-  Maurice Auslander and Oscar Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24. MR 0117252, https://doi.org/10.1090/S0002-9947-1960-0117252-7
-  L. Silver, Noncommutative localizations and applications, J. Algebra 7 (1967), 44–76. MR 0217114, https://doi.org/10.1016/0021-8693(67)90067-1
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Keywords: Order, local ring, separable algebra, irreducible module
Article copyright: © Copyright 1975 American Mathematical Society