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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The Schur group conjecture for the ring of integers of a number field


Author: Peter Nelis
Journal: Proc. Amer. Math. Soc. 114 (1992), 307-318
MSC: Primary 11R21; Secondary 11R18, 16S34, 20C05
MathSciNet review: 1070529
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Abstract: If $ R$ is the ring of $ \mathbb{S}$ integers of a subcyclotomic number field $ K$, then the Schur group conjecture asserts that the Schur group of $ R$ equals the intersection of the Brauer group of $ R$ and the Schur group of $ K$. We prove this assertion in case $ \mathbb{S}$ is the set of all Archimedian primes, i.e. when $ R$ is the ring of integers of $ K$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1070529-X
PII: S 0002-9939(1992)1070529-X
Keywords: Group rings, Azumaya algebras, the integral Brauer group, the Schur group, linear and modular representations
Article copyright: © Copyright 1992 American Mathematical Society