Abstract
In this paper, we characterize when, for any infinite cardinal \(\alpha \), the Fremlin tensor product of two Archimedean Riesz spaces (see Fremlin in Am J Math 94:777–798, 1972) is Dedekind \(\alpha \)-complete. We also provide an example of an ideal I in an Archimedean Riesz space E such that the Fremlin tensor product of I with itself is not an ideal in the Fremlin tensor product of E with itself.
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Acknowledgements
The authors would like to thank Dr. Samuel Lisi for a valuable conversation regarding Sect. 3. We are indebted to Dr. Mohamed Amine Ben Amor for spotting an error in the previous version of Lemma 3.4. In addition, we thank the referee for numerous helpful comments that have improved this paper.
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Buskes, G., Thorn, P. Two results on Fremlin’s Archimedean Riesz space tensor product. Algebra Univers. 84, 21 (2023). https://doi.org/10.1007/s00012-023-00822-8
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DOI: https://doi.org/10.1007/s00012-023-00822-8