2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173202The Stanley's Conjecture on Cohen-Macaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, Soleyman-Jahan and Yassemi. As a consequence of our results Stanley's Conjecture holds in 5 variables.Commutative AlgebraCombinatorics13H10, 13P10, 13C14, 13F20text