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

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- by Lindsay N. Childs PDF
- 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.## References

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## Additional Information

- © Copyright 1975 American Mathematical Society
- 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