A Decomposition of Homomorphic Images of Nearlattices
Ivan Chajda, Miroslav Kolařík · Czech digital mathematics library · 2006
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 $[c) \times (c]$.