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arXiv · 0707.4527

Gr\"obner bases and Betti numbers of monoidal complexes

Winfried Bruns·Robert Koch·Tim Roemer
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Abstract

In this note we consider monoidal complexes and their associated algebras, called toric face rings. These rings generalize Stanley-Reisner rings and affine monoid algebras. We compute initial ideals of the presentation ideal of a toric face ring, and determine its graded Betti numbers. Our results generalize celebrated theorems of Hochster in combinatorial commutative algebra.

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Winfried Bruns, Robert Koch, Tim Roemer. 2007-07-31. Gr\"obner bases and Betti numbers of monoidal complexes. https://doi.org/10.1307/mmj/1220879398

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