Foulis quantales and complete orthomodular lattices
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909486043627520 |
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| author | Botur, Michal Paseka, Jan Smolka, Richard |
| author_facet | Botur, Michal Paseka, Jan Smolka, Richard |
| contents | Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales.
Firstly, given a complete orthomodular lattice X, we associate with it a Foulis quantale Lin(X) consisting of its endomorphisms. This allows us to view X as a left module over Lin(X), thereby introducing a novel fuzzy-theoretic perspective to the study of complete orthomodular lattices.
Conversely, for any Foulis quantale Q, we associate a complete orthomodular lattice [Q] that naturally forms a left Q-module. Furthermore, there exists a canonical homomorphism of Foulis quantales from Q to Lin([Q]). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Foulis quantales and complete orthomodular lattices Botur, Michal Paseka, Jan Smolka, Richard Logic 06F99 Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associate with it a Foulis quantale Lin(X) consisting of its endomorphisms. This allows us to view X as a left module over Lin(X), thereby introducing a novel fuzzy-theoretic perspective to the study of complete orthomodular lattices. Conversely, for any Foulis quantale Q, we associate a complete orthomodular lattice [Q] that naturally forms a left Q-module. Furthermore, there exists a canonical homomorphism of Foulis quantales from Q to Lin([Q]). |
| title | Foulis quantales and complete orthomodular lattices |
| topic | Logic 06F99 |
| url | https://arxiv.org/abs/2502.06350 |