Geodesic
Disjunctive inclusion property in pseudo-complemented distributive lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 233-244.

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Disjunctive inclusion property of several prime ideals and prime filters of pseudo-complemented lattices is studied. Algebraic structures like Boolean algebras and Stone lattices are characterized with the help of the disjunctive inclusion property of prime ideals and prime filters. A set of equivalent conditions is given for every Stone lattice to become a Boolean algebra.
Keywords: disjunctive inclusion property, minimal prime ideal, minimal prime filter, kernel ideal, $\delta $-ideal, Stone lattice, Boolean algebra 
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Sambasiva Rao, M. Disjunctive inclusion property in pseudo-complemented distributive lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 233-244. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a14/

[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] T.S. Blyth, Ideals and filters of pseudo-complemented semi-lattices, Proc. Edin. Math. Soc. 23 (1980) 301–316. https://doi.org/10.1017/S0013091500003850

[4] I. Chajda, R. Halaˇs and J. K¨uhr, Semilattice structures (Heldermann Verlog, Germany, 2007).

[5] S.A. Celani, σ-ideals in distributive pseudo-complemented residuate lattices, Soft Computing 19(7) (2015) 1773–1777.https://doi.org/10.1007/s00500-015-1592-x

[6] W.H. Cornish, Congruences on distributive pseudo-complemented lattices, Bull. Austral. Math. Soc. 8 (1973) 161–179. https://doi.org/10.1017/S0004972700042404

[7] W.H. Cornish, O-ideals, congruences and sheaf representation of distributive lattices, Rev. Roum. Math. Pures. et Appl. 22 (1977) 1059–1067.

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

[9] G. Gratzer, General lattice theory, Academic press (New York, San Francisco, USA, 1978).

[10] 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

[11] M. Sambasiva Rao, Median prime ideals of pseudo-complemented distributive lattices, Archivum Mathematicum 58(4) (2022) 125–136. https://doi.org/10.5817/AM2022-4-213

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

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