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Transactions of the American Mathematical Society
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
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 $ G^{\prime}$ of $ G$ has finite order $ m$ and $ m1(R)$ is invertible in $ R$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0704622-4
PII: S 0002-9947(1983)0704622-4
Article copyright: © Copyright 1983 American Mathematical Society