Geodesic
Ideals, congruences and annihilators on nearlattices
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 46 (2007) no. 1, pp. 25-33.

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By a nearlattice is meant a join-semilattice having the property that every principal filter is a lattice with respect to the semilattice order. We introduce the concept of (relative) annihilator of a nearlattice and characterize some properties like distributivity, modularity or $0$-distributivity of nearlattices by means of certain properties of annihilators.
Classification : 06A12, 06C99, 06D99
Keywords: nearlattice; semilattice; ideal; congruence; distributivity; modularity; $0$-distributivity; annihilator 
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Chajda, Ivan; Kolařík, Miroslav. Ideals, congruences and annihilators on nearlattices. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 46 (2007) no. 1, pp. 25-33. http://geodesic.mathdoc.fr/item/AUPO_2007__46_1_a2/