Effective cowsik-nori theorem for edge ideals

Marilena Crupi; Giancarlo Rinaldo; Naoki Terai; Ken ichi Yoshida

doi:10.1080/00927870903114995

Effective cowsik-nori theorem for edge ideals

Marilena Crupi, Giancarlo Rinaldo, Naoki Terai, Ken ichi Yoshida

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let R = K[x₁, . . ., x_n] be a polynomial ring over a field K. Let I = I(G) ⊆ R be the edge ideal of a graph G. We show that I is complete intersection if R/I^l is Cohen-Macaulay for some l ≥ height I. This strengthens the Cowsik-Nori theorem in the case of edge ideals.

Original language	English
Pages (from-to)	3347-3357
Number of pages	11
Journal	Communications in Algebra
Volume	38
Issue number	9
DOIs	https://doi.org/10.1080/00927870903114995
Publication status	Published - 2010
Externally published	Yes

Keywords

Cohen-macaulay
Complete intersection
Edge ideal
Polarization
Simplicial complex
Symbolic powers

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927870903114995

Cite this

@article{e887a7782e3346c78ee5376bf93c8b4d,

title = "Effective cowsik-nori theorem for edge ideals",

abstract = "Let R = K[x1, . . ., xn] be a polynomial ring over a field K. Let I = I(G) ⊆ R be the edge ideal of a graph G. We show that I is complete intersection if R/Il is Cohen-Macaulay for some l ≥ height I. This strengthens the Cowsik-Nori theorem in the case of edge ideals.",

keywords = "Cohen-macaulay, Complete intersection, Edge ideal, Polarization, Simplicial complex, Symbolic powers",

author = "Marilena Crupi and Giancarlo Rinaldo and Naoki Terai and Yoshida, {Ken ichi}",

note = "Funding Information: The third author acknowledges the financial support of GNSAGA-INDAM and the hospitality during his stay at the Department of Mathematics of the University of Messina (Italy). This work was also supported by KAKENHI18540041 and KAKENHI20540047. We would like to thank the referee for helpful advice.",

year = "2010",

doi = "10.1080/00927870903114995",

language = "English",

volume = "38",

pages = "3347--3357",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "9",

}

TY - JOUR

T1 - Effective cowsik-nori theorem for edge ideals

AU - Crupi, Marilena

AU - Rinaldo, Giancarlo

AU - Terai, Naoki

AU - Yoshida, Ken ichi

N1 - Funding Information: The third author acknowledges the financial support of GNSAGA-INDAM and the hospitality during his stay at the Department of Mathematics of the University of Messina (Italy). This work was also supported by KAKENHI18540041 and KAKENHI20540047. We would like to thank the referee for helpful advice.

PY - 2010

Y1 - 2010

N2 - Let R = K[x1, . . ., xn] be a polynomial ring over a field K. Let I = I(G) ⊆ R be the edge ideal of a graph G. We show that I is complete intersection if R/Il is Cohen-Macaulay for some l ≥ height I. This strengthens the Cowsik-Nori theorem in the case of edge ideals.

AB - Let R = K[x1, . . ., xn] be a polynomial ring over a field K. Let I = I(G) ⊆ R be the edge ideal of a graph G. We show that I is complete intersection if R/Il is Cohen-Macaulay for some l ≥ height I. This strengthens the Cowsik-Nori theorem in the case of edge ideals.

KW - Cohen-macaulay

KW - Complete intersection

KW - Edge ideal

KW - Polarization

KW - Simplicial complex

KW - Symbolic powers

UR - http://www.scopus.com/inward/record.url?scp=77957745752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957745752&partnerID=8YFLogxK

U2 - 10.1080/00927870903114995

DO - 10.1080/00927870903114995

M3 - Article

AN - SCOPUS:77957745752

SN - 0092-7872

VL - 38

SP - 3347

EP - 3357

JO - Communications in Algebra

JF - Communications in Algebra

IS - 9

ER -

Effective cowsik-nori theorem for edge ideals

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this