Two results on Fremlin’s Archimedean Riesz space tensor product

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.