Foulis m-semilattices and their modules
Logic
2025-04-01 v4 Rings and Algebras
Abstract
Building upon the results of Jacobs, we show that the category OMLatLin of orthomodular lattices and linear maps forms a dagger category. For each orthomodular lattice X, we construct a Foulis m-semilattice Lin(X) composed of endomorphisms of X. This m-semilattice acts as a quantale, enabling us to regard X as a left Lin(X)-module. Our novel approach introduces a fuzzy-theoretic dimension to the theory of orthomodular lattices.
Keywords
Cite
@article{arxiv.2501.01405,
title = {Foulis m-semilattices and their modules},
author = {Michal Botur and Jan Paseka and Milan Lekár},
journal= {arXiv preprint arXiv:2501.01405},
year = {2025}
}