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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Orders in separable algebras

Author: Richard B. Tarsy
Journal: Proc. Amer. Math. Soc. 49 (1975), 43-46
MSC: Primary 16A16
MathSciNet review: 0364333
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Abstract: The module $ {P^ \ast }/m{P^ \ast }$, where $ P$ 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, $ {P^ \ast }/m{P^ \ast }$ contains one element from each isomorphism class of irreducible $ P$ modules. Also, in general, if the global dimension of $ P$ is finite, then it equals the homological dimension of $ {P^ \ast }/m{P^ \ast }$.

References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and O. Goldmann, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1-24. MR 22 # 8034. MR 0117252 (22:8034)
  • [2] L. Silver, Noncommutative localizations and applications, J. Algebra 7 (1967), 44-76. MR 36 # 205. MR 0217114 (36:205)

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Keywords: Order, local ring, separable algebra, irreducible module
Article copyright: © Copyright 1975 American Mathematical Society

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