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- \(\{^*\}\) ${\{}^{\ast }\}$ -congruences and principal k- \(\{^*\}\) ${\{}^{\ast }\}$ -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 \(F_{k}(L)\) $F_k(L)$ of all k-filters of L (the lattice \(F_{k}^{p}(L)\) $F_k^p(L)$ principal k-filters of L) and the lattice \(Con^{*}_{k}(L)\) $Co{n}_k^{\ast }(L)$ of all k- \(\{^*\}\) ${\{}^{\ast }\}$ -congruences on L (the lattice \(Con^{*}_{k}(L)\) $Co{n}_k^{\ast }(L)$ of all principal k- \(\{^*\}\) ${\{}^{\ast }\}$ -congruences) of a CRD-Stone algebra L.