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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0382326-9
Keywords: Maximal order, hereditary order, group algebra, Dedekind domain
Article copyright: © Copyright 1975 American Mathematical Society