l-monoid, residuated lattice, orbit, semiring, semimodule, semilinear space

We reconsider the notion of semilinear space and consider it as a couple of two semimodules connected by residuated scalar multiplications. We show that under certain conditions the semigroup of endomorphisms of a semilinear space is a residuated, commutative l-monoid. By this, we obtain what can be regarded as a linear representation of a residuated, commutative l-monoid.