### A decomposition of homomorphic images of nearlattices

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}\left(x\right)=\langle x\vee c,x{\wedge}_{p}c\rangle $ is a (surjective, injective) homomorphism of $\mathcal{S}$ into $\left[c\right)\times \left(c\right]$.