k-filters and k-{∗}-congruences of core regular double Stone algebras

In this paper, we investigate various elegant filters and congruences of the class of core regular double Stone algebras (briefly CRD-Stone algebras). We define and characterize the concepts of k-filters and principal k-filters of a core regular double Stone algebra with the core element k, as well as their algebraic structures. We also look at k-{∗}-congruences and principal k-{∗}-congruences of a CRD-Stone algebra L that are induced by k-filters and principal k-filters of L, respectively. We find an isomorphism between the lattice Fk(L) of all k-filters of L (the lattice Fkp(L) principal k-filters of L) and the lattice Conk∗(L) of all k-{∗}-congruences on L (the lattice Conk∗(L) of all principal k-{∗}-congruences) of a CRD-Stone algebra L. © The Author(s) 2024.