Geodesic
A decomposition of homomorphic images of nearlattices
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 43-51 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice $\mathcal{S}$ and its element $c$ the mapping $\varphi _c(x) = \langle x \vee c, x \wedge _p c \rangle $ is a (surjective, injective) homomorphism of $\mathcal{S}$ into $[c) \times (c]$.
By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice $\mathcal{S}$ and its element $c$ the mapping $\varphi _c(x) = \langle x \vee c, x \wedge _p c \rangle $ is a (surjective, injective) homomorphism of $\mathcal{S}$ into $[c) \times (c]$.
Classification : 06A12, 06B99, 06D99
Keywords: nearlattice; semilattice; distributive element; pseudocomplement; dual pseudocomplement 
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Chajda, Ivan; Kolařík, Miroslav. A decomposition of homomorphic images of nearlattices. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 43-51. http://geodesic.mathdoc.fr/item/AUPO_2006_45_1_a3/

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