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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2510.23094 |
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| _version_ | 1866911234484338688 |
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| author | Liu, Xiaohao Wang, Heyan Chen, Wenjuan |
| author_facet | Liu, Xiaohao Wang, Heyan Chen, Wenjuan |
| contents | Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the number of finite quasi-Boolean algebras and characterize the finite irreducible quasi-Boolean algebras. Second, we show the standard completeness of quasi-Boolean algebras. Finally, we prove that the variety of quasi-Boolean algebras satisfies the congruence extension property and provide a complete characterization of how congruences on a Boolean subalgebra can be extended to the whole quasi-Boolean algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The completeness and congruences of quasi-Boolean algebras Liu, Xiaohao Wang, Heyan Chen, Wenjuan Logic Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the number of finite quasi-Boolean algebras and characterize the finite irreducible quasi-Boolean algebras. Second, we show the standard completeness of quasi-Boolean algebras. Finally, we prove that the variety of quasi-Boolean algebras satisfies the congruence extension property and provide a complete characterization of how congruences on a Boolean subalgebra can be extended to the whole quasi-Boolean algebra. |
| title | The completeness and congruences of quasi-Boolean algebras |
| topic | Logic |
| url | https://arxiv.org/abs/2510.23094 |