Geodesic
Generalized prime $D$-filters of distributive lattices
Archivum mathematicum, Tome 57 (2021) no. 3, pp. 157-174
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The concept of generalized prime $D$-filters is introduced in distributive lattices. Generalized prime $D$-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime $D$-filters is introduced in distributive lattices and properties of minimal prime $D$-filters are then studied with respect to congruences. Some topological properties of the space of all prime $D$-filters of a distributive lattice are also studied.
The concept of generalized prime $D$-filters is introduced in distributive lattices. Generalized prime $D$-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime $D$-filters is introduced in distributive lattices and properties of minimal prime $D$-filters are then studied with respect to congruences. Some topological properties of the space of all prime $D$-filters of a distributive lattice are also studied.
DOI : 10.5817/AM2021-3-157
Classification : 06D99
Keywords: dense element; filter; $D$-filter; prime $D$-filter; congruence; Hausdorff space 
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Phaneendra Kumar, A.P.; Sambasiva Rao, M.; Sobhan Babu, K. Generalized prime $D$-filters of distributive lattices. Archivum mathematicum, Tome 57 (2021) no. 3, pp. 157-174. doi: 10.5817/AM2021-3-157

[1] Birkhoff, G.: Lattice theory. Amer. Math. Soc. Colloq. XXV, Providence, USA, 1967. | MR | Zbl

[2] Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra. Springer Verlag, 1981. | MR | Zbl

[3] Cornish, W.H.: Normal lattices. J. Aust. Math. Soc. 14 (1972), 200–215. | DOI | MR

[4] Cornish, W.H.: Annulets and $\alpha $-ideals in distributive lattices. J. Aust. Math. Soc. 15 (1973), 70–77. | DOI | MR

[5] Cornish, W.H.: Quasicomplemented lattices. Comment. Math. Univ. Carolin. 15 (3) (1974), 501–511. | MR

[6] Katrinak, T.: Remarks on Stone lattices, I. Math.-Fyz.Časopis 16 (1966), 128–142. | MR

[7] Kist, J.: Minimal prime ideals in commutative semigroups. Proc. London Math. Soc. Sec. B 13 (1963), 31–50. | DOI | MR

[8] Mandelker, M.: Relative annihilators in lattices. Duke Math. J. 37 (1970), 377–386. | DOI | MR | Zbl

[9] Phaneendra Kumar, A.P., Sambasiva Rao, M., Sobhan Babu, K.: Filters of distributive lattices generated by dense elements. to appear in Palestine J. Math.

[10] Sambasiva Rao, M.: $e$-filters of MS-algebras. Acta Math. Sci. 33B (3) (2013), 738–746. | DOI | MR

[11] Sambasiva Rao, M., Badawy, A.: $\mu $-filters of distributive lattices. Southeast Asian Bull. Math. 40 (2016), 251–264. | MR

[12] Speed, T.P.: Some remarks on a class of distributive lattices. J. Aust. Math. Soc. 9 (1969), 289–296. | DOI | MR

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