  Every 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.
