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Keywords:
dense element; filter; $D$-filter; prime $D$-filter; congruence; Hausdorff space
dense element; filter; $D$-filter; prime $D$-filter; congruence; Hausdorff space
Summary:
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.
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