Foulis-Holland theorem for implicative-orthomodular lattices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866913282220097536 |
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| author | Ciungu, Lavinia Corina |
| author_facet | Ciungu, Lavinia Corina |
| contents | We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the distributive implicative-orthomodular lattices. Moreover, we define the center of an implicative-orthomodular lattice as the set of all elements that commute with all other elements, and we prove that the center is an implicative-Boolean algebra. Additionally, we give new characterizations of implicative-orthomodular lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Foulis-Holland theorem for implicative-orthomodular lattices Ciungu, Lavinia Corina Logic We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the distributive implicative-orthomodular lattices. Moreover, we define the center of an implicative-orthomodular lattice as the set of all elements that commute with all other elements, and we prove that the center is an implicative-Boolean algebra. Additionally, we give new characterizations of implicative-orthomodular lattices. |
| title | Foulis-Holland theorem for implicative-orthomodular lattices |
| topic | Logic |
| url | https://arxiv.org/abs/2403.16762 |