2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65416Let K be the face ring of the independence complex of a matroid. We show that if T is a generic linear system of parameters, then K/T satisfies a weak form of the Hard Lefschetz Theorem. As a result, the first half of the h-vector of the complex satisfies inequalities similar to the g-theorem for simplicial polytopes.6 pages. Will appear in J. Comb. Theory Ser. BCombinatoricsCommutative Algebra05B35 (Primary) 13F55 (Secondary)text