2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75354After [J.Herzog, D.Popescu, Finite filtrations of modules and shellable multicomplexes, Preprint IMAR no 4/2005, Bucharest, 2005], the shellability of multicomplexes $Γ$ is given in terms of some special faces of $Γ$ called facets. Here we give a criterion for the shellability in terms of maximal facets. Multigraded pretty clean filtration is the algebraic counterpart of a shellable multicomplex. We give also a criterion for the existence of a multigraded pretty clean filtration.10 pagesCommutative AlgebraCombinatorics13C14;16W70;13C13;05E99text