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Transactions of the American Mathematical Society

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Maximal orders over regular local rings


Author: Mark Ramras
Journal: Trans. Amer. Math. Soc. 155 (1971), 345-352
MSC: Primary 16.20
DOI: https://doi.org/10.1090/S0002-9947-1971-0272808-3
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.


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

  • [1] M. Auslander and O. Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1-24. MR 22 #8034. MR 0117252 (22:8034)
  • [2] -, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367-409. MR 22 #12130. MR 0121392 (22:12130)
  • [3] M. Deuring, Algebren, Springer, Berlin, 1935. MR 0228526 (37:4106)
  • [4] M. Harada, Hereditary orders, Trans. Amer. Math. Soc. 107 (1963), 273-290. MR 27 #1474. MR 0151489 (27:1474)
  • [5] M. Ramras, Maximal orders over regular local rings of dimension two, Trans. Amer. Math. Soc. 142 (1969), 457-479. MR 39 #6878. MR 0245572 (39:6878)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0272808-3
Keywords: Maximal order, central simple algebra, conductor, global dimension, regular local ring, reflexive module
Article copyright: © Copyright 1971 American Mathematical Society

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