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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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