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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


Authors: L. N. Childs, G. Garfinkel and M. Orzech
Journal: Trans. Amer. Math. Soc. 175 (1973), 299-326
MSC: Primary 13A20
MathSciNet review: 0349652
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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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DOI: https://doi.org/10.1090/S0002-9947-1973-0349652-3
Keywords: Brauer group of a commutative ring, separable algebra, Azumaya algebra, graded algebra, Galois extension of a commutative ring, graded Galois extension, graded tensor product, smash product
Article copyright: © Copyright 1973 American Mathematical Society