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

DOI:
https://doi.org/10.1090/S0002-9947-1994-1250816-9

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:
https://doi.org/10.1090/S0002-9947-1994-1250816-9

Article copyright:
© Copyright 1994
American Mathematical Society