Some basic properties of graded Azumaya algebras are given systematically. Here, the grading is indexed by an arbitrary additive group and the notion of a graded Azumaya algebra is relative to a choice of a commutation factor. We also establish two exact sequences which generalize the Skolem-Noether theorem.
"Azumaya algebras with general gradings and their automorphisms." Tsukuba J. Math. 23 (2) 293 - 320, October 1999. https://doi.org/10.21099/tkbjm/1496163874