Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC