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Cohen-Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals

Constantinescu, A ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1080/00927872.2014.897550
  3. Publisher: Taylor and Francis Inc , 2015
  4. Abstract:
  5. Let K{double-struck} be a field, and let R = K{double-struck}[x1,.., xn] be the polynomial ring over K{double-struck} in n indeterminates x1,.., xn. Let G be a graph with vertex-set {x1,.., xn}, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J(k) and J[k], respectively. In this paper, we give necessary and sufficient conditions for R/Jk, R/J (k), and R/J [k] to be Cohen-Macaulay. We also study the limit behavior of the depths of these rings
  6. Keywords:
  7. Bracket power ; Cohen-Macaulay module ; Cover ideal ; Depth of a module ; Symbolic power
  8. Source: Communications in Algebra ; Volume 43, Issue 1 , Aug , 2015 , Pages 143-157 ; 00927872 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/00927872.2014.897550