Computing the Brauer group of graded Azumaya algebras from its subgroups (Q1073877)

For a connected commutative ring R with identity and G a finite abelian group, \textit{F. W. Long} [Proc. Lond. Math. Soc., III. Ser. 29, 237-256 (1974; Zbl 0294.13003)] introduced a generalized Brauer group of algebras with a G-grading upon which G acts as a group of grade-preserving automorphisms. The author investigates the structure of BD(R,G) for noncyclic G. The cyclic case was previously studied by several authors. A sample result which the author proves is the following. She introduces a subgroup \({\mathcal A}\) of central algebras with trivial action cocycle and shows that \({\mathcal A}\cong BC(R,G)\times BT(R,G)\); where BC(R,G) is the subgroup of classes for which a representative has trivial action, and BT(R,G) is a subgroup isomorphic to Aut(G).