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

Mohsen Nourany; Shokoofeh Ghorbani; Arsham Borumand Saeid

doi:10.18778/0138-0680.2024.13

Authors

Mohsen Nourany Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iran https://orcid.org/0009-0002-6632-0851
Shokoofeh Ghorbani Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iran https://orcid.org/0000-0002-3724-8654
Arsham Borumand Saeid Shahid Bahonar University of Kerman, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Kerman, Iran https://orcid.org/0000-0001-9495-6027

DOI:

https://doi.org/10.18778/0138-0680.2024.13

Keywords:

SDWH-algebra, open filter, deductive system, congruence kernel, weakly regular

Abstract

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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