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Transactions of the American Mathematical Society

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

 

 

Local orders whose lattices are direct sums of ideals


Author: Jeremy Haefner
Journal: Trans. Amer. Math. Soc. 321 (1990), 717-740
MSC: Primary 16H05
DOI: https://doi.org/10.1090/S0002-9947-1990-0978384-3
MathSciNet review: 978384
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Abstract: Let $ R$ be a complete local Dedekind domain with quotient field $ K$ and let $ \Lambda $ be a local $ R$-order in a separable $ K$-algebra. This paper classifies those orders $ \Lambda $ such that every indecomposable $ R$-torsionfree $ \Lambda $-module is isomorphic to an ideal of $ \Lambda $. These results extend to the noncommutative case some results for commutative rings found jointly by this author and L. Levy.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0978384-3
Article copyright: © Copyright 1990 American Mathematical Society