Geodesic
$\sigma$-filters of distributive lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 261-276

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The concept of σ-filters is introduced in distributive lattices and studied some properties of these classes of filters. Two sets of equivalent conditions are derived one for every μ-filter to become a σ-filter and the other for every filter to become a σ-filter of a distributive lattice. A one-to-one correspondence is established between the set of all prime σ-filters of a distributive lattice and the set of all prime σ-filters of its quotient lattice with respect to a congruence.
Keywords: prime filter, co-annihilator, $\mu$-filter, O-filter, $\sigma$-filter, pm-lattice 
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Sambasiva Rao, M. $\sigma$-filters of distributive lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 261-276. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a1/