Gröbner bases and Betti numbers of monoidal complexes

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.

18 pages

References in corpus (1)

• On toric face rings

Cited by in corpus (4)

• Algebra retracts and Stanley-Reisner rings
• Seminormality and local cohomology of toric face rings
• On some local cohomology spectral sequences
• The geometry and combinatorics of cographic toric face rings