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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Lodz University Press
2024-06-01
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| Series: | Bulletin of the Section of Logic |
| Subjects: | |
| Online Access: | https://czasopisma.uni.lodz.pl/bulletin/article/view/22007 |
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| Summary: | 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. |
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| ISSN: | 0138-0680 2449-836X |