Tensor products of Bands and Ideals

TL;DR

This paper investigates the Riesz tensor product of ideals and bands in Riesz spaces, proving that the Dedekind completion of such a tensor product of two ideals remains an ideal, thus advancing the understanding of their structural properties.

Contribution

It provides a definitive answer to an open question about the behavior of the Riesz tensor product of ideals and bands, including the Dedekind completion property.

Findings

Dedekind completion of the tensor product of two ideals is an ideal

Provides new insights into the structure of Riesz tensor products

Addresses an open question in the theory of Riesz spaces

Abstract

In this study we give an answer to the open question about the Riesz tensor product of ideals and bands of a Riesz space. We prove among other results that the Dedekind completion of the Riesz tensor product of two ideals is again an ideal.