Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras
In 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 lea...
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| Format: | Article |
| Language: | English |
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Lodz University Press
2024-06-01
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| Series: | Bulletin of the Section of Logic |
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| Online Access: | https://czasopisma.uni.lodz.pl/bulletin/article/view/22007 |
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| author | Mohsen Nourany Shokoofeh Ghorbani Arsham Borumand Saeid |
| author_facet | Mohsen Nourany Shokoofeh Ghorbani Arsham Borumand Saeid |
| author_sort | Mohsen Nourany |
| collection | DOAJ |
| description | In 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. |
| format | Article |
| id | doaj-art-7629f21804514e61bcc8e8488ac6de23 |
| institution | Kabale University |
| issn | 0138-0680 2449-836X |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Bulletin of the Section of Logic |
| spelling | doaj-art-7629f21804514e61bcc8e8488ac6de232025-02-07T07:22:48ZengLodz University PressBulletin of the Section of Logic0138-06802449-836X2024-06-0153445547710.18778/0138-0680.2024.1322106Open Filters and Congruence Relations on Self-Distributive Weak Heyting AlgebrasMohsen Nourany0https://orcid.org/0009-0002-6632-0851Shokoofeh Ghorbani1https://orcid.org/0000-0002-3724-8654Arsham Borumand Saeid2https://orcid.org/0000-0001-9495-6027Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iran Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iran Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iran In 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.https://czasopisma.uni.lodz.pl/bulletin/article/view/22007sdwh-algebraopen filterdeductive systemcongruence kernelweakly regular |
| spellingShingle | Mohsen Nourany Shokoofeh Ghorbani Arsham Borumand Saeid Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras Bulletin of the Section of Logic sdwh-algebra open filter deductive system congruence kernel weakly regular |
| title | Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras |
| title_full | Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras |
| title_fullStr | Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras |
| title_full_unstemmed | Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras |
| title_short | Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras |
| title_sort | open filters and congruence relations on self distributive weak heyting algebras |
| topic | sdwh-algebra open filter deductive system congruence kernel weakly regular |
| url | https://czasopisma.uni.lodz.pl/bulletin/article/view/22007 |
| work_keys_str_mv | AT mohsennourany openfiltersandcongruencerelationsonselfdistributiveweakheytingalgebras AT shokoofehghorbani openfiltersandcongruencerelationsonselfdistributiveweakheytingalgebras AT arshamborumandsaeid openfiltersandcongruencerelationsonselfdistributiveweakheytingalgebras |