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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Jacobson radical of a CSL algebra


Authors: Kenneth R. Davidson and John Lindsay Orr
Journal: Trans. Amer. Math. Soc. 344 (1994), 925-947
MSC: Primary 47D25
MathSciNet review: 1250816
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Abstract: Extrapolating from Ringrose's characterization of the Jacobson radical of a nest algebra, Hopenwasser conjectured that the radical of a CSL algebra coincides with the Ringrose ideal (the closure of the union of zero diagonal elements with respect to finite sublattices). A general interpolation theorem is proved that reduces this conjecture for completely distributive lattices to a strictly combinatorial problem. This problem is solved for all width two lattices (with no restriction of complete distributivity), verifying the conjecture in this case.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1250816-9
PII: S 0002-9947(1994)1250816-9
Article copyright: © Copyright 1994 American Mathematical Society