Cohen-Macaulay quotients of normal semigroup rings via irreducible resolutions [article]

Ezra Miller
2001 arXiv   pre-print
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
more » ... n spectral sequence, thereby also providing a combinatorial topological version for polyhedral cell complexes, involving no commutative algebra.
arXiv:math/0110096v1 fatcat:kgnpki6375hprdblhjlgelco7e