2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122204Given a multigraded algebra $A$, it is a natural question whether or not for two homogeneous components $A_u$ and $A_v$, the product $A_{nu}A_{nv}$ is the whole component $A_{nu+nv}$ for $n$ big enough. We give combinatorial and geometric answers to this question.Minor changes, 7 pages, to appear in Math. Res. LettCommutative AlgebraAlgebraic Geometry13A02, 14L24text