Geodesic
Median filters of pseudo-complemented distributive lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 147-161.

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Coherent filters, strongly coherent filters, and τ-closed filters are introduced in pseudo-complemented distributive lattices and their characterization theorems are derived. A set of equivalent conditions is derived for every filter of a pseudo-complemented distributive lattice to become a coherent filter. The notion of median filters is introduced and some equivalent conditions are derived for every maximal filter of a pseudo-complemented distributive lattice to become a median filter which leads to a characterization of Stone lattices.
Keywords: coherent filter, strongly coherent filter, median filter, minimal prime filter, maximal filter, Stone lattice 
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Sambasiva Rao, M. Median filters of pseudo-complemented distributive lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 147-161. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a9/

[1] R. Balbes and A. Horn, Stone lattices, Duke Math. J. 37 (1970) 537–545.

[2] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. XXV (Providence, USA, 1967).

[3] I. Chajda, R. Halaš and J. Kűhr, Semilattice Structures (Heldermann Verlag, Germany, 2007).

[4] W.H. Cornish, Congruences on distributive pseudo-complemented lattices, Bull. Austral. Math. Soc. 8 (1973) 167–179.

[5] O. Frink, Pseudo-complements in semi-lattices, Duke Math. J. 29 (1962) 505–514. https://doi.org/10.1215/S0012-7094-62-02951-4

[6] G. Gr¨atzer, General Lattice Theory, Academic Press (New York, San Francisco, USA, 1978).

[7] M. Sambasiva Rao, δ-ideals in pseudo-complemented distributive lattices, Archivum Mathematicum 48(2) (2012) 97–105. https://doi.org/10.5817/AM2012-2-97

[8] A.P. Paneendra Kumar, M. Sambasiva Rao, and K. Sobhan Babu, Generalized prime D-filters of distributive lattices, Archivum Mathematicum 57(3) (2021) 157–174. https://doi.org/10.5817/AM2021-3-157

[9] T.P. Speed, On Stone lattices, Jour. Aust. Math. Soc. 9(3-4) (1969) 297–307. https://doi.org/10.1017/S1446788700007217

[10] M.H. Stone, A theory of representations for Boolean algebras, Tran. Amer. Math. Soc. 40 (1936) 37–111. https://doi.org/10.2307/1989664