k-filters and k-$$\{^*\}$$-congruences of core regular double Stone algebras

Abstract

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 $$F_{k}(L)$$ 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 $$Con^{*}_{k}(L)$$ C o n k ∗ ( L ) of all k-$$\{^*\}$$ { ∗ } -congruences on L (the lattice $$Con^{*}_{k}(L)$$ C o n k ∗ ( L ) of all principal k-$$\{^*\}$$ { ∗ } -congruences) of a CRD-Stone algebra L.