Free vector lattices and free vector lattice algebras
Abstract
We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in universal algebra. A discussion about free -algebras over non-empty sets is given, where the main issues appear to be open. It is indicated how the existence results for free vector lattices and vector lattice algebras can be used for easy proofs of existence results for free Banach lattices and free Banach lattice algebras. A detailed exposition of the necessary material from universal algebra is included.
Keywords
Cite
@article{arxiv.2005.00902,
title = {Free vector lattices and free vector lattice algebras},
author = {Marcel de Jeu},
journal= {arXiv preprint arXiv:2005.00902},
year = {2024}
}
Comments
37 pages. Some typos corrected. Final version, to be published in 2021 by Birkh\"auser in `Positivity and its Applications', Proceedings of the Positivity X conference from 8-12 July 2019 in Pretoria. The paper is dedicated to the memory of Coenraad Labuschagne