Semigroup rings and simplicial complexes

Autor(en): Bruns, W 
Herzog, J
Stichwörter: IDEALS; Mathematics; Mathematics, Applied; RESOLUTIONS
Erscheinungsdatum: 1997
Herausgeber: ELSEVIER SCIENCE BV
Journal: JOURNAL OF PURE AND APPLIED ALGEBRA
Volumen: 122
Ausgabe: 3
Startseite: 185
Seitenende: 208
Zusammenfassung: 
We study the minimal free resolution F of a ring T = S/I where S is a positive affine semigroup ring over a field K, and I is an ideal in S generated by monomials. We will essentially use the fact that the multigraded Betti numbers of T can be computed from the relative homology of simplicial complexes that we shall call squarefree divisor complexes. In a sense, these simplicial complexes represent the divisibility relations in S if one neglects the multiplicities with which the irreducible elements appear in the representation of an element. In Section 1 we study the dependence of the free resolution on the characteristic of K. In Section 2 we show that, up to an equivalence in homotopy, every simplicial complex can be `realized' in a normal semigroup ring and also in a one-dimensional semigroup ring. Furthermore, we describe all the graphs among the squarefree divisor complexes. In Section 3 we deduce assertions about certain simplicial complexes of chessboard type from information about free resolutions of well-understood semigroup rings. (C) 1997 Elsevier Science B.V.
ISSN: 00224049
DOI: 10.1016/S0022-4049(97)00051-0

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