A Certain Class of Filters in Generalized Complemented Distributive Lattices (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce $K^g$-filters jointly  derived from the class of ideals and the class of generalized complementations  in a generalized complemented distributive lattice. We obtain some algebraic properties on the obtained class, and we provide some counter-examples. Mainly we derive some Boolean algebras (distributive lattices) through the class of $K^g-$filters in a generalized complemented distributive lattice. Finally, we introduce normal $K^g$-filters in a generalized complemented distributive lattice and then prove that the class of normal $K^g$-filters is a Boolean algebra.
Keywords: Filters; Distributive lattices; Ideals