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

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Document Type : Research Paper

Authors

1 Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 102

2 Department of Mathematics, MVGR College of Engineering, Vizianagaram, India-535 005

Abstract

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.

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 17 June 2025

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