Homomorphisms and subalgebras of free convex semilattices

A convex semilattices is a convex algebra endowed with an additional semilattice operation that satisfies a distributive law. We investigate free convex semilattices by studying the homomorphisms into products RΩ and, more specifically, the homomorphisms between two free finitely generated convex semilattices. We characterise the finitely generated subalgebras of a free finitely generated convex semilattice.