Group Rings which are Azumaya Algebras

Abstract

Abstract. The group ring RG of a group G over a ring R (with identity \(R)) is a separable algebra over its center if and only if the following conditions hold:(a) R is a separable algebra over its center; (b) the center of G has finite index in G: (c) the commutator subgroup G' of G has finite order m and m\(R) is invertiblein R.

Azumaya algebras in skew group rings

“…Then a relation among the group ring RG, the group algebra CG and R was given by F. R. DeMeyer and G. J. Janusz ( [5]). That is, RG is an Azumaya algebra if and only if so are R and CG.…”