Cohen–Macaulay quotients of normal semigroup rings via irreducible resolutions
2002; International Press of Boston; Volume: 9; Issue: 1 Linguagem: Inglês
10.4310/mrl.2002.v9.n1.a9
ISSN1945-001X
Autores Tópico(s)Algebraic structures and combinatorial models
ResumoFor a radical monomial ideal I in a normal semigroup ring k [Q], there is a unique minimal irreducible resolution 0where theprime ideals.This paper characterizes Cohen-Macaulay quotients k[Q]/I as those whose minimal irreducible resolutions are linear, meaning that W i is pure of dimension dim(k[Q]/I)i for i ≥ 0. The proof exploits a graded ring-theoretic analogue of the Zeeman spectral sequence [Zee63], thereby also providing a combinatorial topological version involving no commutative algebra.The characterization via linear irreducible resolutions reduces to the Eagon-Reiner theorem [ER98] by Alexander duality when Q = N d .
Referência(s)