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Transactions of the American Mathematical Society

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

 

 

The Brauer group of graded Azumaya algebras. II. Graded Galois extensions


Author: Lindsay N. Childs
Journal: Trans. Amer. Math. Soc. 204 (1975), 137-160
MSC: Primary 13A20
DOI: https://doi.org/10.1090/S0002-9947-1975-0364216-5
MathSciNet review: 0364216
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Abstract: This paper continues the study of the Brauer group $ {B_\phi }(R,G)$ of $ G$-graded Azumaya $ R$-algebras begun in [5]. A group $ {\operatorname{Galz} _\phi }(R,G)$ of graded Galois extensions is constructed which always contains, and often equals, the cokernel of $ {B_\phi }(R,G)$ modulo the usual Brauer group of $ R$. Sufficient conditions for equality are found. The structure of $ {\operatorname{Galz} _\phi }(R,G)$ is studied, and $ {\operatorname{Galz} _\phi }(R,{(Z/{p^e}Z)^r})$ is computed. These results are applied to give computations of a Brauer group of dimodule algebras constructed by F. W. Long.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0364216-5
Article copyright: © Copyright 1975 American Mathematical Society