Cohen-Macaulay and (S2) properties of the second power of squarefree monomial ideals

Do Trong Hoang; Giancarlo Rinaldo; Naoki Terai

doi:10.3390/math7080684

Cohen-Macaulay and (S₂) properties of the second power of squarefree monomial ideals

Do Trong Hoang, Giancarlo Rinaldo, Naoki Terai

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We show that Cohen-Macaulay and (S₂) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S/I² satisfies the Serre condition (S₂₎, but is not Cohen-Macaulay.

Original language	English
Article number	684
Journal	Mathematics
Volume	7
Issue number	8
DOIs	https://doi.org/10.3390/math7080684
Publication status	Published - 2019

Keywords

(S) condition
Cohen-Macaulay
Edge ideal
Stanley-Reisner ideal

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.3390/math7080684

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abstract = "We show that Cohen-Macaulay and (S2) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S/I2 satisfies the Serre condition (S2), but is not Cohen-Macaulay.",

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