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

UR - http://www.scopus.com/inward/record.url?scp=84905263426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905263426&partnerID=8YFLogxK

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 -