## The Brauer group of graded Azumaya algebras

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- by L. N. Childs, G. Garfinkel and M. Orzech PDF
- Trans. Amer. Math. Soc.
**175**(1973), 299-326 Request permission

## Abstract:

We study*G*-graded Azumaya

*R*-algebras for

*R*a commutative ring and

*G*a finite abelian group, and a Brauer group formed by such algebras. A short exact sequence is obtained which relates this Brauer group with the usual Brauer group of

*R*and with a group of graded Galois extensions of

*R*. In case

*G*is cyclic a second short exact sequence describes this group of graded Galois extensions in terms of the usual group of Galois extensions of

*R*with group

*G*and a certain group of functions on ${\text {Spec}}(R)$.

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## Additional Information

- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**175**(1973), 299-326 - MSC: Primary 13A20
- DOI: https://doi.org/10.1090/S0002-9947-1973-0349652-3
- MathSciNet review: 0349652