Cohen-Macaulay quotients of normal semigroup rings via irreducible resolutions

Details Cohen-Macaulay quotients of normal semigroup rings via irreducible resolutions Cohen-Macaulay quotients of normal semigroup rings via irreducible resolutions

2001-10-09

arxiv.org/abs/math/0110096v1

Mathematics

Commutative Algebra

9 pages, no figures

Scientific paper

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.

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