Topological Characterization of α-Filters in Paradistributive Latticoids

Kola, Satyanarayana Rao; Rao, G. Nanaji; Rafi, Noorbhasha; Sirisetti, Ramesh; Gaketem, Thiti

doi:10.28924/2291-8639-24-2026-194

Research Article

Topological Characterization of α-Filters in Paradistributive Latticoids

Satyanarayana Rao Kola
G. Nanaji Rao
Noorbhasha Rafi
Ramesh Sirisetti
Thiti Gaketem*

* Corresponding author

Abstract

We study topological properties of the space of prime $\alpha$-filters of a paradistributive latticoid. Using the hull-kernel topology we characterize compactness, separation axioms ($T_{0},T_{1}$, Hausdorff), and relate minimality of prime $\alpha$-filters to topological properties. Several equivalent conditions for minimality are obtained and relationships to annulets and direct factors are discussed. Examples and consequences for various classes of latticoids are indicated.

How to Cite

S. R. Kola, G. N. Rao, N. Rafi, R. Sirisetti, T. Gaketem, Topological Characterization of α-Filters in Paradistributive Latticoids, Int. J. Anal. Appl. 24 (2026), 194. https://doi.org/10.28924/2291-8639-24-2026-194

BibTeX

@article{Kola2026,
  author  = {Kola, Satyanarayana Rao and Rao, G. Nanaji and Rafi, Noorbhasha and Sirisetti, Ramesh and Gaketem, Thiti},
  title   = {Topological Characterization of α-Filters in Paradistributive Latticoids},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {194},
  doi     = {10.28924/2291-8639-24-2026-194}
}

References

[1] S. Ajjarapu, R. Bandaru, R. Shukla, Y.B. Jun, Parapseudo-Complementation on Paradistributive Latticoids, Eur. J. Pure Appl. Math. 17 (2024), 1129–1145. https://doi.org/10.29020/nybg.ejpam.v17i2.5042.
[2] S. Ajjarapu, R. Bandaru, R.R. Kotha, R. Shukla, Topological Properties of Prime Filters and Minimal Prime Filters on a Paradistributive Latticoid, Int. J. Math. Math. Sci. 2024 (2024), 1862245. https://doi.org/10.1155/ijmm/1862245.
[3] R. Bandaru, P. Patel, N. Rafi, R. Shukla, S. Ajjarapu, Normal Paradistributive Latticoids, Eur. J. Pure Appl. Math. 17 (2024), 1306–1320. https://doi.org/10.29020/nybg.ejpam.v17i2.5127.
[4] R. Bandaru, S. Ajjarapu, Paradistributive Latticoids, Eur. J. Pure Appl. Math. 17 (2024), 819–834. https://doi.org/10.29020/nybg.ejpam.v17i2.5125.
[5] G. Birkhoff, Lattice Theory, American Mathematical Society, Providence, 1967.
[6] I. Calomino, Quasicomplemented Distributive Nearlattices, arXiv:2504.01124, 2025. https://doi.org/10.48550/arXiv.2504.01124.
[7] I. Chajda, H. L\"{a}nger, Filters and Ideals in Pseudocomplemented Posets, arXiv:2202.03166, 2022. https://doi.org/10.48550/arXiv.2202.03166.
[8] I. Chajda, M. Kolař\'{i}k, H. L\"{a}nger, Special Filters in Bounded Lattices, arXiv:2306.09958, 2023. https://doi.org/10.48550/arXiv.2306.09958.
[9] B.A. Davey, H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press, 2002.
[10] J. Gunda, R. Sirisetti, R. Bandaru, R. Shukla, G-Filters and Generalized Complemented Distributive Lattices, Eur. J. Pure Appl. Math. 18 (2025), 5490. https://doi.org/10.29020/nybg.ejpam.v18i1.5490.
[11] Y.L.T. Jeufack, L. Kwuida, Filters and Congruences in Weakly Complemented Lattices, arXiv:2510.04960, 2025. https://doi.org/10.48550/arXiv.2510.04960.
[12] C. Nag, Coherent Ideals of 1-Distributive Lattices, Malaya J. Mat. 13 (2025), 54–62. https://doi.org/10.26637/mjm1301/007.
[13] S. Ramesh, G. Chinnayya, G. Jogarao, R. Bandaru, A. Iampan, Hierarchy Elements in an Almost Distributive Lattice, Eur. J. Pure Appl. Math. 17 (2024), 1691–1704. https://doi.org/10.29020/nybg.ejpam.v17i3.5226.
[14] A.A. Khabyah, N. Rafi, M.A. Ansari, Exploring Star Filters of Almost Distributive Lattices, Axioms 14 (2025), 96. https://doi.org/10.3390/axioms14020096.
[15] S.K. Rao, R. Sirisetti, R. Bandaru, N. Rafi, A. Iampan, $\alpha$-Filters in Paradistributive Latticoids, Int. J. Anal. Appl. Communicated.
[16] U. Swamy, G.C. Rao, Almost Distributive Lattices, J. Aust. Math. Soc. Ser. A 31 (1981), 77–91. https://doi.org/10.1017/S1446788700018498.