2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144240Let $J\subset I$ be monomial ideals. We show that the Stanley depth of $I/J$ can be computed in a finite number of steps. We also introduce the $\fdepth$ of a monomial ideal which is defined in terms of prime filtrations and show that it can also be computed in a finite number of steps. In both cases it is shown that these invariants can be determined by considering partitions of suitable finite posets into intervals.Commutative Algebra13C13, 13C14, 05E99, 16W70text