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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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On the ideal structure of Banach algebras
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by William E. Dietrich PDF
Trans. Amer. Math. Soc. 169 (1972), 59-74 Request permission

Abstract:

For Banach algebras $A$ in a class which includes all group and function algebras, we show that the family of ideals of $A$ with the same hull is typically quite large, containing ascending and descending chains of arbitrary length through any ideal in the family, and that typically a closed ideal of $A$ whose hull meets the Šilov boundary of $A$ cannot be countably generated algebraically.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 169 (1972), 59-74
  • MSC: Primary 46J20; Secondary 43A20, 46J10
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0308791-2
  • MathSciNet review: 0308791