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/

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

[2] T.S. Blyth, Ideals and filters of Pseudo-complemented semilattices, Proc. Edinburgh Math. Soc. 23 (1980) 301–316. doi:10.1017/S0013091500003850

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

[4] G. Gratzer, General Lattice Theory (Academic Press, New York, 1978).

[5] K.B. Lee, Equational class of distributive pseudo-complemented lattices, Canad. J. Math. 22 (1970) 881–891. doi:10.4153/CJM-1970-101-4

[6] G.C. Rao and S. Ravikumar, Minimal prime ideals in almost distributive lattices, Int. J. Contemp. Math. Sci. 4 (10) (2009) 475–484. http://m-hikari.com/ijcms-password2009/9-12-2009/raoIJCMS9-12-2009-3.pdf

[7] M.S. Rao, Kernel ideals in Almost Distributive Lattices, Asian-European J. Math. 5 (2) (2012), 1250024(11 pages). doi:10.1142/S1793557112500246

[8] H.P. Sankappanavar, Semi-de Morgan algebras, J. Symbolic Logic 52 (3) (1987) 712–724. doi:10.2307/2274359

[9] U.M. Swamy, G.C. Rao and G. Nanaji Rao, Pseudo-complementation on Almost Distributive Lattices, South. Asian Bull. Math. 24 (2000) 95–104. doi:10.1007/s10012-000-0095-5

[10] U.M. Swamy, G.C. Rao and G. Nanaji Rao, Stone Almost Distributive Lattices, South. Asian Bull. Math. 27 (3) (2003) 115–119. http://www.seams-bull-math.ynu.edu.cn/archive.jsp

[11] U.M. Swamy and G.C. Rao, Almost Distributive Lattices, J. Australian. Math. Soc. Ser. A 31 (1981) 77–91. doi:10.1017/S1446788700018498