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New Classes of Set-theoretic Complete Intersection Monomial Ideals |
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| Authors: | M R Pournaki S A Seyed Fakhari S Yassemi |
| Institution: | 1. Department of Mathematical Sciences , Sharif University of Technology , Tehran , Iran;2. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran , Iran pournaki@ipm.ir;4. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran , Iran;5. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran , Iran;6. School of Mathematics, Statistics and Computer Science, College of Science , University of Tehran , Tehran , Iran |
| Abstract: | Let Δ be a simplicial complex and χ be an s-coloring of Δ. Biermann and Van Tuyl have introduced the simplicial complex Δχ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of Δχ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of Δχ over a field is set-theoretic complete intersection. This also generalizes a result of Macchia. |
| Keywords: | Arithmetical rank Lyubeznik resolution s-Coloring Set-theoretic complete intersection ideal Simplicial complex |