Algebraic geometry for l-groups

Abstract. In this paper we focus on the algebraic geometry of the variety of l-groups (i.e. lattice ordered abelian groups). In particular we study the role of the introduction of constants in functional spaces and l-polynomial spaces, which are themselves l-groups, evaluated over other l-groups. We use different tools and techniques, with an increasing level of abstraction, to describe properties of l-groups, topological spaces (with the Zariski topology) and a formal logic, all linked by the underlying theme of solutions of l-equations.