Geodesic
On Quasi-P-Almost Distributive Lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 5-19

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In this paper, the concept of quasi pseudo-complementation on an Almost Distributive Lattice (ADL) as a generalization of pseudo-complementation on an ADL is introduced and its properties are studied. Necessary and su cient conditions for a quasi pseudo-complemented ADL(q-p-ADL) to be a pseudo-complemented ADL(p-ADL) and Stone ADL are derived and the set S(L) = a* | a ∈ L is proved to be a Boolean algebra. Also, the notions of ∗−congruence and kernel ideals are introduced in a quasi-p-ADL and characterized kernel ideals. Finally, some equivalent conditions are given for every ideal of a quasi-p-ADL to be a kernel ideal.
Keywords: pseudo-complementation, quasi pseudo-complementation, Almost Distributive Lattice (ADL), p-ADL, quasi-p-ADL 
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Bandaru, Ravi Kumar; Rao, G.C. On Quasi-P-Almost Distributive Lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a0/