Foulis m-semilattices and their modules

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Authors	BOTUR Michal PASEKA Jan LEKÁR Milan
Year of publication	2025
Type	Article in Proceedings
Conference	2025 IEEE 55th International Symposium on Multiple-Valued Logic (ISMVL)
MU Faculty or unit	Faculty of Science
Citation
web	https://www.computer.org/csdl/proceedings-article/ismvl/2025/074400a196/27EbG45NrGw
Doi	https://doi.org/10.1109/ISMVL64713.2025.00044
Keywords	quantale; quantale module; orthomodular lattice; linear map; Sasaki projection; Foulis m-semilattice; msemilattice module
Description	Building upon 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.
Related projects:	Specifický výzkum v odborné, aplikované a učitelské matematice 2024 Orthogonality and symmetry