The space of prime \pi-filters of almost distributive lattices

The concepts have been presented in Almost Distributive Lattices (ADLs), namely, regular filters and \pi-filters. A set of conditions has been identified that are equivalent to becoming an \mathcal{D}-filter into a regular filter. Moreover, it has been shown that for any \mathcal{D}-filter, there is a homomorphism with a dense kernel, which is itself a regular filter. The characterization of \pi-filters in relation to congruences and regular filters has been established. Additionally, equivalent conditions have been derived to show that the space containing all prime filters forms a Hausdorff space.

کلیدواژه ها:

Almost distributive lattices ، Hausdorff space ، Minimal prime \mathcal{D}-filter ، \pi-filter ، Regular filter