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New Classes of Set-theoretic Complete Intersection Monomial Ideals

Pournaki, M. R ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1080/00927872.2014.934462
  3. Publisher: Taylor and Francis Inc , 2015
  4. Abstract:
  5. 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
  6. Keywords:
  7. Arithmetical rank ; Lyubeznik resolution ; s-Coloring ; Set-theoretic complete intersection ideal ; Simplicial complex
  8. Source: Communications in Algebra ; Volume 43, Issue 9 , Jun , 2015 , Pages 3920-3924 ; 00927872 (ISSN)
  9. URL: http://www.tandfonline.com/doi/full/10.1080/00927872.2014.934462