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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Schur subgroup of the Brauer group of cyclotomic rings of integers
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by C. Riehm PDF
Proc. Amer. Math. Soc. 103 (1988), 27-30 Request permission

Abstract:

Let $K$ be a finite abelian extension of the rational numbers $\mathbb {Q}$. Let ${\mathbf {S}}$ be a finite set of primes of $K$ including the infinite ones, and let $\mathfrak {o}$ be the ring of ${\mathbf {S}}$-integers in $K$. Then the Schur subgroup $S(\mathfrak {o})$ of the Brauer group $B(\mathfrak {o})$ is defined, in analogy with $S(K)$, via representations of finite groups on finitely generated projective $\mathfrak {o}$-modules. It is easy to see that $S(\mathfrak {o}) \subseteq S(K) \cap B(\mathfrak {o})$. We shall show that there is equality in the case of $K$ a purely cyclotomic extension $\mathbb {Q}({\varepsilon _m})$ of $\mathbb {Q}$ (where ${\varepsilon _m}$ is an $m$th root of 1).
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 27-30
  • MSC: Primary 13A20; Secondary 11S25, 12E15, 20C10
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0938638-X
  • MathSciNet review: 938638