Foulis m-semilattices and their modules
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917970854281216 |
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| author | Botur, Michal Paseka, Jan Lekár, Milan |
| author_facet | Botur, Michal Paseka, Jan Lekár, Milan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Foulis m-semilattices and their modules Botur, Michal Paseka, Jan Lekár, Milan Logic Rings and Algebras 06F99 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. |
| title | Foulis m-semilattices and their modules |
| topic | Logic Rings and Algebras 06F99 |
| url | https://arxiv.org/abs/2501.01405 |