 We will henceforth assume that every Riesz space and every vector lattice is an ordered vector space but that a preordered vector lattice is not necessarily partially ordered.If "E" is an ordered vector space over formula_1 with positive whose positive cone "C" is generating (i.e.such that "E" = "C" - "C"), and if for every "x", "y" ∈ "C" either formula_2 or formula_3 exists, then "E" is a vector lattice.