Orders in separable algebras
HTML articles powered by AMS MathViewer
- by Richard B. Tarsy PDF
- Proc. Amer. Math. Soc. 49 (1975), 43-46 Request permission
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
- 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
- L. Silver, Noncommutative localizations and applications, J. Algebra 7 (1967), 44–76. MR 217114, DOI 10.1016/0021-8693(67)90067-1
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 43-46
- MSC: Primary 16A16
- DOI: https://doi.org/10.1090/S0002-9939-1975-0364333-5
- MathSciNet review: 0364333