Geodesic
$\alpha $-ideals and annihilator ideals in 0-distributive lattices
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 1, pp. 63-74.

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In a 0-distributive lattice sufficient conditions for an $\alpha $-ideal to be an annihilator ideal and prime ideal to be an $\alpha $-ideal are given. Also it is proved that the images and the inverse images of $\alpha $-ideals are $\alpha $-ideals under annihilator preserving homomorphisms.
Classification : 06D99
Keywords: 0-distributive lattice; $\alpha $-ideal; annihilator ideal; quasi-complemented lattice 
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Pawar, Y. S.; Khopade, S. S. $\alpha $-ideals and annihilator ideals in 0-distributive lattices. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 1, pp. 63-74. http://geodesic.mathdoc.fr/item/AUPO_2010__49_1_a6/