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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Ideal theory in $ f$-algebras


Authors: C. B. Huijsmans and B. de Pagter
Journal: Trans. Amer. Math. Soc. 269 (1982), 225-245
MSC: Primary 06F25; Secondary 46A40, 46J20, 54C40
MathSciNet review: 637036
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637036-5
PII: S 0002-9947(1982)0637036-5
Keywords: Riesz spaces, uniformly complete, normal, order ideal, orthomorphism, $ f$-algebra, algebra ideal, idempotent, semiprime, pseudoprime, prime ideal
Article copyright: © Copyright 1982 American Mathematical Society