2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221844Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial ideals. The paper includes experiments showing good performance in practice.25 pages, 8 figures. See http://www.broune.com/ for the data usedCommutative AlgebraCombinatorics13P99 (Primary) 05E99, 11Y99 (Secondary)text