A note on order complete $f$-algebras
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- by Boris LavriΔ PDF
- Proc. Amer. Math. Soc. 100 (1987), 414-418 Request permission
Abstract:
Let $A$ be an Archimedean uniformly complete $f$-algebra with unit element. Then the following conditions are equivalent (i) $A$ is order complete. (ii) Every regular algebra ideal in $A$ is an order ideal. (iii) Every finitely generated regular algebra ideal in $A$ is a principal algebra ideal. The proof is based on the fact that the range of every injective orthomorphism in an order complete Riesz space is an order ideal.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 414-418
- MSC: Primary 06F25; Secondary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1987-0891137-5
- MathSciNet review: 891137