Quotient quantum-Wajsberg algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910427778121728 |
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| author | Ciungu, Lavinia Corina |
| author_facet | Ciungu, Lavinia Corina |
| contents | We define and study the notions of q-deductive systems, p-deductive systems, deductive systems, maximal and strongly maximal q-deductive systems in quantum-Wajsberg algebras. We also introduce the notion of congruences induced by deductive systems of a quantum-Wajsberg algebra, and we show that there is a relationship between congruences and deductive systems. Furthermore, we define the quotient quantum-Wajsberg algebra with respect to a deductive system, and prove that the quotient quantum-Wajsberg algebra is locally finite if and only if the deductive system is strongly maximal. Finally, we define the weakly linear and quasi-linear quantum-Wajsberg algebras, and give a characterization of weakly linear quotient quantum-Wajsberg algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01845 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quotient quantum-Wajsberg algebras Ciungu, Lavinia Corina Quantum Algebra We define and study the notions of q-deductive systems, p-deductive systems, deductive systems, maximal and strongly maximal q-deductive systems in quantum-Wajsberg algebras. We also introduce the notion of congruences induced by deductive systems of a quantum-Wajsberg algebra, and we show that there is a relationship between congruences and deductive systems. Furthermore, we define the quotient quantum-Wajsberg algebra with respect to a deductive system, and prove that the quotient quantum-Wajsberg algebra is locally finite if and only if the deductive system is strongly maximal. Finally, we define the weakly linear and quasi-linear quantum-Wajsberg algebras, and give a characterization of weakly linear quotient quantum-Wajsberg algebras. |
| title | Quotient quantum-Wajsberg algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2304.01845 |