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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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Ideal theory in $f$-algebras
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by C. B. Huijsmans and B. de Pagter PDF
Trans. Amer. Math. Soc. 269 (1982), 225-245 Request permission

Abstract:

The paper deals mainly with the theory of algebra ideals and order ideals in $f$-algebras. Necessary and sufficient conditions are established for an algebra ideal to be prime, semiprime or idempotent. In a uniformly complete $f$-algebra with unit element every algebra ideal is an order ideal iff the $f$-algebra is normal. This result is based on the fact that the range of every orthomorphism in a uniformly complete normal Riesz space is an order ideal.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 269 (1982), 225-245
  • MSC: Primary 06F25; Secondary 46A40, 46J20, 54C40
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0637036-5
  • MathSciNet review: 637036