JOURNAL ARTICLE

The spectra of quasi-Boolean algebras.

  • Published In: Logic Journal of the IGPL, 2024, v. 32, n. 1. P. 139 1 of 3

  • Database: Business Source Ultimate 2 of 3

  • Authored By: Lv, Yajie; Chen, Wenjuan 3 of 3

Abstract

The article introduces quasi-Boolean algebras (QB-algebras) as a generalization of Boolean algebras within the framework of quasi-lattices, motivated by developments in quantum computation and non-classical logics. It systematically develops the theory of QB-algebras, including their defining properties, filters, prime and maximal filters, and the correspondence between filters and filter congruences. The prime spectrum of a QB-algebra is shown to form a compact Hausdorff topological space under the Zariski topology. Finally, the paper defines the reticulation of a QB-algebra as a Boolean algebra obtained via a natural congruence relation, establishing an isomorphism between the filter lattices of the QB-algebra and its reticulation, and demonstrating a homeomorphism between their prime spectra.

Additional Information

  • Source:Logic Journal of the IGPL. 2024/02, Vol. 32, Issue 1, p139
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2024
  • ISSN:1367-0751
  • DOI:10.1093/jigpal/jzac073
  • Accession Number:175416577
  • Copyright Statement:Copyright of Logic Journal of the IGPL is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.