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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Unimaximal orders


Author: T. V. Fossum
Journal: Proc. Amer. Math. Soc. 52 (1975), 99-102
MSC: Primary 16A18
DOI: https://doi.org/10.1090/S0002-9939-1975-0382326-9
MathSciNet review: 0382326
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Abstract: Let $R$ be a Dedekind domain with quotient field $K$, and let $A$ be a separable $K$-algebra. An $R$-order $\Lambda$ in $A$ is said to be unimaximal if $\Lambda$ is contained in a unique maximal $R$-order in $A$. Unimaximal orders are given characterizations which are applied to determine those finite groups $G$ of order $n$ for which $RG$ is unimaximal, where $K$ is an algebraic number field containing a primitive $n$th root of unity.


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Keywords: Maximal order, hereditary order, group algebra, Dedekind domain
Article copyright: © Copyright 1975 American Mathematical Society