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Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras

dc.contributor.authorNourany, Mohsen
dc.contributor.authorGhorbani, Shokoofeh
dc.contributor.authorBorumand Saeid, Arsham
dc.date.accessioned2025-02-05T13:36:54Z
dc.date.available2025-02-05T13:36:54Z
dc.date.issued2024-06-21
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/54523
dc.description.abstractIn this paper, we study (open) filters and deductive systems of self-distributive weak Heyting algebras (SDWH-algebras) and obtain some results which determine the relationship between them. We show that the variety of SDWH-algebras is not weakly regular and every open filter is the kernel of at least one congruence relation. Finally, we characterize those SDWH-algebras which are weakly regular by using some properties involving principal congruence relations.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;4en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectSDWH-algebraen
dc.subjectopen filteren
dc.subjectdeductive systemen
dc.subjectcongruence kernelen
dc.subjectweakly regularen
dc.titleOpen Filters and Congruence Relations on Self-Distributive Weak Heyting Algebrasen
dc.typeArticle
dc.page.number455-477
dc.contributor.authorAffiliationNourany, Mohsen - Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iranen
dc.contributor.authorAffiliationGhorbani, Shokoofeh - Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iranen
dc.contributor.authorAffiliationBorumand Saeid, Arsham - Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iranen
dc.identifier.eissn2449-836X
dc.referencesM. Alizadeh, N. Joharizadeh, Counting weak Heyting algebras on finite distributive lattices, Logic Journal of the IGPL, vol. 23(2) (2015), pp. 247–258, DOI: https://doi.org/10.1093/jigpal/jzu033en
dc.referencesM. Ardeshir, W. Ruitenburg, Basic propositional calculus I, Mathematical Logic Quarterly, vol. 44(3) (1998), pp. 317–343, DOI: https://doi.org/10.1002/malq.19980440304en
dc.referencesG. Birkhoff, Lattice theory, vol. 25, American Mathematical Soc. (1940).en
dc.referencesS. Celani, R. Jansana, Bounded distributive lattices with strict implication, Mathematical Logic Quarterly, vol. 51(3) (2005), pp. 219–246, DOI: https://doi.org/10.1002/malq.200410022en
dc.referencesI. Chajda, Weakly regular lattices, Mathematica Slovaca, vol. 35(4) (1985), pp. 387–391.en
dc.referencesI. Chajda, Congruence kernels in weakly regular varieties, Southeast Asian Bulletin of Mathematics, vol. 24 (2000), pp. 15–18, DOI: https://doi.org/10.1007/s10012-000-0015-8en
dc.referencesP. Dehornoy, Braids and self-distributivity, vol. 192, Birkhäuser (2012), DOI: https://doi.org/10.1007/978-3-0348-8442-6.en
dc.referencesA. Diego, Sur les algebras de Hilbert, Ed. Herman, Collection de Logique Mathématique. Serie A, vol. 21 (1966).en
dc.referencesG. Epstein, A. Horn, Logics which are characterized by subresiduated lattices, Mathematical Logic Quarterly, vol. 22(1) (1976), pp. 199–210, DOI: https://doi.org/10.1002/malq.19760220128en
dc.referencesS. Ghorbani, MULTIPLIERS IN WEAK HEYTING ALGEBRAS, Journal of Mahani Mathematics Research, vol. 13(3) (2024), pp. 33–46, DOI: https://doi.org/10.22103/jmmr.2024.22758.1563en
dc.referencesD. Joyce, A classifying invariant of knots, the knot quandle, Journal of Pure and Applied Algebra, vol. 23(1) (1982), pp. 37–65, DOI: https://doi.org/10.1016/0022-4049(82)90077-9en
dc.referencesH. Junji, Congruence relations and congruence classes in lattices, Osaka Mathematical Journal, vol. 15(1) (1963), pp. 71–86.en
dc.referencesM. Nourany, S. Ghorbani, A. B. Saeid, On self-distributive weak Heyting algebras, Mathematical Logic Quarterly, vol. 69(2) (2023), pp. 192–206, DOI: https://doi.org/10.1002/malq.202200073en
dc.referencesH. J. San Martín, Compatible operations on commutative weak residuated lattices, Algebra universalis, vol. 73 (2015), pp. 143–155, DOI: https://doi.org/10.1007/s00012-015-0317-4en
dc.referencesH. J. San Martín, Principal congruences in weak Heyting algebras, Algebra universalis, vol. 75 (2016), pp. 405–418, DOI: https://doi.org/10.1007/s00012-016-0381-4en
dc.referencesH. J. San Martín, On congruences in weak implicative semi-lattices, Soft Computing, vol. 21 (2017), pp. 3167–3176, DOI: https://doi.org/10.1007/s00500-016-2188-9en
dc.referencesA. Visser, A propositional logic with explicit fixed points, Studia Logica, (1981), pp. 155–175, DOI: https://doi.org/10.1007/BF01874706en
dc.contributor.authorEmailNourany, Mohsen - nourany@gmail.com
dc.contributor.authorEmailGhorbani, Shokoofeh - sh.ghorbani@uk.ac.ir
dc.contributor.authorEmailBorumand Saeid, Arsham - arsham@uk.ac.ir
dc.identifier.doi10.18778/0138-0680.2024.13
dc.relation.volume53


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