## The Jacobson radical of a CSL algebra

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- by Kenneth R. Davidson and John Lindsay Orr PDF
- Trans. Amer. Math. Soc.
**344**(1994), 925-947 Request permission

## 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.## References

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## Additional Information

- © Copyright 1994 American Mathematical Society
- 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