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- Title
The spectra of quasi-Boolean algebras.
- Authors
Lv, Yajie; Chen, Wenjuan
- Abstract
In the present paper, we introduce the notions of quasi-Boolean algebras as the generalization of Boolean algebras. First we discuss the related properties of quasi-Boolean algebras. Second we define filters of quasi-Boolean algebras and investigate some properties of filters in quasi-Boolean algebras. We also show that there is a one-to-one correspondence between the set of filters and the set of filter congruences on a quasi-Boolean algebra. Then we investigate the prime filters and maximal filters of quasi-Boolean algebras, showing that the prime filters of a quasi-Boolean algebra are precisely the maximal filters and the prime spectrum of a quasi-Boolean algebra is a compact Hausdorff topological space. Finally, we define and study the reticulation of a quasi-Boolean algebra.
- Publication
Logic Journal of the IGPL, 2024, Vol 32, Issue 1, p139
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzac073