Group rings which are Azumaya algebras

DeMeyer, F. R.; Janusz, G. J.

doi:10.1090/S0002-9947-1983-0704622-4

Group rings which are Azumaya algebras
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by F. R. DeMeyer and G. J. Janusz

Trans. Amer. Math. Soc. 279 (1983), 389-395

DOI: https://doi.org/10.1090/S0002-9947-1983-0704622-4

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Abstract:

The group ring $RG$ of a group $G$ over a ring $R$ (with identity $1(R)$) 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 $m1(R)$ is invertible in $R$.

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