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Proceedings of the American Mathematical Society

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

 
 

 

The maximal ideals in quaternion orders


Author: John A. Riley
Journal: Proc. Amer. Math. Soc. 28 (1971), 436-438
MSC: Primary 16.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0274489-7
MathSciNet review: 0274489
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Abstract: Let $ R$ be a Noetherian, integrally closed local domain, and $ \Lambda $ an $ R$-order in a generalized quaternion algebra over the quotient field of $ R$. In this note, it is proved that: (a) $ \Lambda $ has at most two maximal ideals; and (b) in case $ \Lambda $ does have exactly two maximal ideals, the corresponding residue class rings are commutative fields.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274489-7
Keywords: Orders in quaternion algebras, orders in simple algebras, quaternion algebras, maximal ideals, radical of an order
Article copyright: © Copyright 1971 American Mathematical Society

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