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

Childs, Lindsay N.

doi:10.1090/S0002-9947-1975-0364216-5

The Brauer group of graded Azumaya algebras. II. Graded Galois extensions
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Trans. Amer. Math. Soc. 204 (1975), 137-160 Request permission

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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