فهرست نشریات علمی دسترسی آزاد ایران

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.