2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60620We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation to initial ideals of lattice ideals.19 pages, 2 figuresCombinatoricstext