TY - JOUR
T1 - Cohen-Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals
AU - Constantinescu, A.
AU - Pournaki, M. R.
AU - Seyed Fakhari, S. A.
AU - Terai, N.
AU - Yassemi, S.
N1 - Funding Information:
The research of M. R. Pournaki, S. A. Seyed Fakhari, and S. Yassemi was in part supported by a grant from IPM (No. 92130115, No. 92130422, and No. 92130214).
PY - 2015/1
Y1 - 2015/1
N2 - 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.
AB - 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.
KW - Bracket power
KW - Cohen-Macaulay module
KW - Cover ideal
KW - Depth of a module
KW - Symbolic power
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U2 - 10.1080/00927872.2014.897550
DO - 10.1080/00927872.2014.897550
M3 - Article
AN - SCOPUS:84905263426
SN - 0092-7872
VL - 43
SP - 143
EP - 157
JO - Communications in Algebra
JF - Communications in Algebra
IS - 1
ER -