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

A. Constantinescu, M. R. Pournaki, S. A. Seyed Fakhari, N. Terai, S. Yassemi

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)143-157
Number of pages15
JournalCommunications in Algebra
Volume43
Issue number1
DOIs
Publication statusPublished - Jan 2015
Externally publishedYes

Keywords

  • Bracket power
  • Cohen-Macaulay module
  • Cover ideal
  • Depth of a module
  • Symbolic power

ASJC Scopus subject areas

  • Algebra and Number Theory

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