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

Shokoofeh Ghorbani; Mohsen Nourany; Arsham Borumand Saeid

doi:10.18778/0138-0680.2024.13

Authors

Shokoofeh Ghorbani Department of Pure Mathematics https://orcid.org/0000-0002-3724-8654
Mohsen Nourany https://orcid.org/0009-0002-6632-0851
Arsham Borumand Saeid https://orcid.org/0000-0001-9495-6027

DOI:

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

Keywords:

SDWH-algebras, open filters, 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. Then it presents necessary and sufficient conditions for the existence of a one to one correspondence between open filters and congruence relations.

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