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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A cohomological approach to the Brauer-Long group and the groups of Galois extensions and strongly graded rings
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by S. Caenepeel and M. Beattie PDF
Trans. Amer. Math. Soc. 324 (1991), 747-775 Request permission

Abstract:

Let $G$ be a finite abelian group, and $R$ a commutative ring. The Brauer-Long group $\operatorname {BD} (R,G)$ is described by an exact sequence \[ 1 \to {\operatorname {BD} ^s}(R,G) \to \operatorname {BD} (R,G)\xrightarrow {\beta }\operatorname {Aut} (G \times {G^{\ast }})(R)\] where ${\operatorname {BD} ^s}(R,G)$ is a product of étale cohomology groups, and Im $\beta$ is a kind of orthogonal subgroup of $\operatorname {Aut} (G \times {G^{\ast }})(R)$. This sequence generalizes some other well-known exact sequences, and restricts to two split exact sequences describing Galois extensions and strongly graded rings.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 747-775
  • MSC: Primary 16H05; Secondary 13A20
  • DOI: https://doi.org/10.1090/S0002-9947-1991-0987160-8
  • MathSciNet review: 987160