New Classes of Set-theoretic Complete Intersection Monomial Ideals

Abstract

Let Δ be a simplicial complex and χ be an s-coloring of Δ. Biermann and Van Tuyl have introduced the simplicial complex Δ_χ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of Δ_χ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of Δ_χ over a field is set-theoretic complete intersection. This also generalizes a result of Macchia.

Key Words:

• Arithmetical rank
• Lyubeznik resolution
• s-Coloring
• Set-theoretic complete intersection ideal
• Simplicial complex

2010 Mathematics Subject Classification:

• 13F55
• 13A15

ACKNOWLEDGMENT

The authors would like to thank the referee for a careful reading of this note and for valuable comments.

Notes

Communicated by G. Leuschke.