The Brauer group of graded Azumaya algebras

Childs, L. N.; Garfinkel, G.; Orzech, M.

doi:10.1090/S0002-9947-1973-0349652-3

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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Lectures on algebraic K-theory

Éléments de mathématique

Algèbre commutative

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