$k$-ideals and $k$-\( \{^+ \} \)-congruences of core regular double Stone algebras

In this paper, the authors study many interesting properties of ideals and congruences of the class of a core regular double Stone algebra (briefly $CRD$-Stone algebra). We introduce and characterize the concepts of $k$-ideals and principal $k$-ideals of a core regular double Stone algebra with the core element $k$ and establish the algebraic structures of such ideals. Also, we investigate $k$-\( \{^+ \} \)-congruences and principal $k$-\( \{^+ \} \)-congruences of a $CRD$-Stone algebra $L$ which are induced by $k$-ideals and principal $k$-ideals of $L$, respectively. We obtain an isomorphism between the lattice of $k$-ideals (principal $k$-ideals) and the lattice of $k$-\( \{^+ \} \)-congruences (principal $k$-\( \{^+ \} \)-congruences) of a $CRD$-Stone algebra. We provide some examples to clarify the basic results of this article.