Maximal orders over regular local rings
HTML articles powered by AMS MathViewer
- by Mark Ramras PDF
- Trans. Amer. Math. Soc. 155 (1971), 345-352 Request permission
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
- Maurice Auslander and Oscar Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24. MR 117252, DOI 10.1090/S0002-9947-1960-0117252-7
- Maurice Auslander and Oscar Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409. MR 121392, DOI 10.1090/S0002-9947-1960-0121392-6
- Max Deuring, Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 41, Springer-Verlag, Berlin-New York, 1968 (German). Zweite, korrigierte auflage. MR 0228526
- Manabu Harada, Hereditary orders, Trans. Amer. Math. Soc. 107 (1963), 273–290. MR 151489, DOI 10.1090/S0002-9947-1963-0151489-9
- Mark Ramras, Maximal orders over regular local rings of dimension two, Trans. Amer. Math. Soc. 142 (1969), 457–479. MR 245572, DOI 10.1090/S0002-9947-1969-0245572-2
Additional Information
- © Copyright 1971 American Mathematical Society
- 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