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Keywords:
nearlattice; semilattice; distributive element; pseudocomplement; dual pseudocomplement
nearlattice; semilattice; distributive element; pseudocomplement; dual pseudocomplement
Summary:
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 $[c) \times (c]$.
References:
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