Generalized prime $D$-filters of distributive lattices

Abstract

The concept of generalized prime D-filters is introduced in distributive lattices. Generalized prime D-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime D-filters is introduced in distributive lattices and properties of minimal prime D-filters are then studied with respect to congruences. Some topological properties of the space of all prime D-filters of a distributive lattice are also studied.