2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62353Every quotient R/I of a semigroup ring R by a radical monomial ideal I has a unique minimal injective-like resolution by direct sums of quotients of R modulo prime monomial ideals. The quotient R/I is Cohen-Macaulay if and only if every summand in cohomological degree $i$ has dimension exactly dim(R/I) - i. This Cohen-Macaulay characterization reduces to the Eagon-Reiner theorem by Alexander duality when R is a polynomial ring. The proof exploits a graded ring-theoretic generalization of the Zeeman spectral sequence, thereby also providing a combinatorial topological version for polyhedral cell complexes, involving no commutative algebra.9 pages, no figuresCommutative AlgebraAlgebraic TopologyCombinatorics13C14, 14M05, 13D02, 55Txx (primary) 14M25, 13F55 (secondary)text