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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Group rings which are Azumaya algebras


Authors: F. R. DeMeyer and G. J. Janusz
Journal: Trans. Amer. Math. Soc. 279 (1983), 389-395
MSC: Primary 16A16; Secondary 16A26, 16A27
DOI: https://doi.org/10.1090/S0002-9947-1983-0704622-4
MathSciNet review: 704622
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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 $Gā€™$ of $G$ has finite order $m$ and $m1(R)$ is invertible in $R$.


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Article copyright: © Copyright 1983 American Mathematical Society