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Proceedings of the American Mathematical Society

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

 

 

Central separable algebras which are locally endomorphism rings of free modules


Author: Bernice L. Auslander
Journal: Proc. Amer. Math. Soc. 30 (1971), 395-404
MSC: Primary 13.15
DOI: https://doi.org/10.1090/S0002-9939-1971-0285517-7
MathSciNet review: 0285517
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Abstract: The object of this paper is to study the kernel of the map of the Brauer group of an integrally closed noetherian domain A into the direct product of the Brauer groups of the localizations of A at prime ideals. It is shown that this kernel is isomorphically contained in the torsion subgroup of the first cohomology group of the sheaf of Cartier divisors over Spec A. As a consequence, the author describes several new sets of conditions on A which guarantee that the kernel is trivial.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0285517-7
Keywords: Integrally closed noetherian domain, localization at prime ideals, prime spectrum, sheaf of Cartier divisors, semilocal domain, local unique factorization domain
Article copyright: © Copyright 1971 American Mathematical Society