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

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10.1080/00927870903236186

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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",

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AU - Terai, Naoki

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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

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

Abstract

Keywords

ASJC Scopus subject areas

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