Centers of quantum-Wajsberg algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910553421643776 |
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| author | Ciungu, Lavinia Corina |
| author_facet | Ciungu, Lavinia Corina |
| contents | We define the Wajsberg-center and the OML-center of a quantum-Wajsberg algebra, and study their structures. We prove that the Wajsberg-center is a Wajsberg subalgebra of a quantum-Wajsberg algebra, and that it is a distributive sublattice of its corresponding poset. If the quantum-Wajsberg algebra is quasi-linear, we show that the Wajsberg-center is a linearly ordered Wajsberg algebra. We also show that the lattice subreduct of the Wajsberg-center is a Kleene algebra. Furthermore, we prove that the OML-center is an orthomodular lattice, and the orthomodular lattices form a subvariety of the variety of quantum-Wajsberg algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02483 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Centers of quantum-Wajsberg algebras Ciungu, Lavinia Corina Logic We define the Wajsberg-center and the OML-center of a quantum-Wajsberg algebra, and study their structures. We prove that the Wajsberg-center is a Wajsberg subalgebra of a quantum-Wajsberg algebra, and that it is a distributive sublattice of its corresponding poset. If the quantum-Wajsberg algebra is quasi-linear, we show that the Wajsberg-center is a linearly ordered Wajsberg algebra. We also show that the lattice subreduct of the Wajsberg-center is a Kleene algebra. Furthermore, we prove that the OML-center is an orthomodular lattice, and the orthomodular lattices form a subvariety of the variety of quantum-Wajsberg algebras. |
| title | Centers of quantum-Wajsberg algebras |
| topic | Logic |
| url | https://arxiv.org/abs/2311.02483 |