2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77880Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley-Reisner complex. Reverse lexicographic initial ideals of generic lattice ideals are generic. Cohen-Macaulayness for cogeneric ideals is characterized combinatorially; in the cogeneric case the Cohen-Macaulay type is greater than or equal to the number of irreducible components. Methods of proof include Alexander duality and Stanley's theory of local h-vectors.15 pages, LaTeXCommutative AlgebraAlgebraic GeometryCombinatorics13D02, 13H10, 13P10 (Primary); 52B20, 05E99 (Secondary)text