On the separation of convex sets in some idempotent semimodules

Two linear maps are usually needed to separate disjoint convex subsets of an idempotent semimodule. In the context of Max-Plus convexity separation can be achieved by a single map if one considers linear maps with values in a linearly ordered semimodule, whose construction is given here, which is not the Max-Plus semiring R∪{-∞}.