Maximal lattice-free convex sets in linear subspaces

We consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also show that these sets are polyhedra. The latter result extends a theorem of Lov'asz characterizing maximal lattice-free convex sets in ${\mathbb{R}}^n$.