Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone

Margherita Barile; Naoki Terai

doi:10.1080/00927870903236186

Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone

Margherita Barile, Naoki Terai

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

9 Citations (Scopus)

Abstract

When a cone is added to a simplicial complex Δ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ′ equals the projective dimension of the Stanley-Reisner ring of Δ′ if the corresponding equality holds for Δ.

Original language	English
Pages (from-to)	3686-3698
Number of pages	13
Journal	Communications in Algebra
Volume	38
Issue number	10
DOIs	https://doi.org/10.1080/00927870903236186
Publication status	Published - Oct 2010
Externally published	Yes

Keywords

Arithmetical rank
Monomial ideals
Projective dimension
Set-theoretic complete intersections

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927870903236186

Fingerprint Dive into the research topics of 'Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone'. Together they form a unique fingerprint.

Cite this

@article{573d947eae774368819f65dc4d689bf2,

title = "Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone",

abstract = "When a cone is added to a simplicial complex Δ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ′ equals the projective dimension of the Stanley-Reisner ring of Δ′ if the corresponding equality holds for Δ.",

keywords = "Arithmetical rank, Monomial ideals, Projective dimension, Set-theoretic complete intersections",

author = "Margherita Barile and Naoki Terai",

year = "2010",

month = oct,

doi = "10.1080/00927870903236186",

language = "English",

volume = "38",

pages = "3686--3698",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "10",

}

TY - JOUR

T1 - Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone

AU - Barile, Margherita

AU - Terai, Naoki

PY - 2010/10

Y1 - 2010/10

N2 - When a cone is added to a simplicial complex Δ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ′ equals the projective dimension of the Stanley-Reisner ring of Δ′ if the corresponding equality holds for Δ.

AB - When a cone is added to a simplicial complex Δ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ′ equals the projective dimension of the Stanley-Reisner ring of Δ′ if the corresponding equality holds for Δ.

KW - Arithmetical rank

KW - Monomial ideals

KW - Projective dimension

KW - Set-theoretic complete intersections

UR - http://www.scopus.com/inward/record.url?scp=78649683046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649683046&partnerID=8YFLogxK

U2 - 10.1080/00927870903236186

DO - 10.1080/00927870903236186

M3 - Article

AN - SCOPUS:78649683046

VL - 38

SP - 3686

EP - 3698

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 10

ER -

Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this