G-filters and Generalized Complemented Distributive Lattices (European Journal of Pure and Applied Mathematics, 2025)
In this work, we derive a class of filters (G-filters, normal G-filters, and co-dense filters) in a distributive lattice (with dense elements). We also verify the various algebraic properties of these filters. It is observed that the set of co-dense filters forms an uninduced distributive lattice, and the set of G-filters forms a Boolean algebra. We characterize quasi-complemented distributive lattices using G-filters and normal G-filters. Using normal G-filters, we demonstrate several necessary and sufficient requirements for a distributive lattice to become quasi-complemented. Also, we introduce generalized complementation on a distributive lattice and characterize it in terms of quasi-complemented distributive lattices.
Keywords: Dense elements; Filters; G-filters; Normal G-filters; quasi-complemented distributive lattices; generalized complemented distributive lattices