Gröbner bases and Betti numbers of monoidal complexes

Details Gröbner bases and Betti numbers of monoidal complexes Gröbner bases and Betti numbers of monoidal complexes

2007-07-31

arxiv.org/abs/0707.4527v1

Mich. Math. J. 57, 71-91 (2008)

Mathematics

Commutative Algebra

18 pages

Scientific paper

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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