2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168706Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial ideals. The purpose of this survey is to gather the developments into one location, with self-contained proofs, including direct combinatorial topological connections between them.19 pages, for proceedings of the Conference on Combinatorial Commutative Algebra and Computer Algebra (Mangalia, Romania, May 2008)Commutative AlgebraCombinatoricstext