A note on monomial ideals which are Cohen–Macaulay in a fixed codimension

M. R. Pournaki; K. Shibata; N. Terai; S. Yassemi

doi:10.1080/00927872.2022.2079663

A note on monomial ideals which are Cohen–Macaulay in a fixed codimension

M. R. Pournaki, K. Shibata, N. Terai, S. Yassemi

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

Abstract

In this note, we introduce and investigate the notion of (Formula presented.) monomial ideals. We give an explicit relation of the (Formula presented.) property to a monomial ideal and its polarization. Further, we characterize the (Formula presented.) property of the ordinary as well as the symbolic third or more powers of squarefree monomial ideals.

Original language	English
Journal	Communications in Algebra
DOIs	https://doi.org/10.1080/00927872.2022.2079663
Publication status	Accepted/In press - 2022

Keywords

CM simplicial complex
Cohen–Macaulay ring
Cohen–Macaulay simplicial complex
generalized Cohen–Macaulay ring
generalized Cohen–Macaulay simplicial complex
simplicial complex

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2022.2079663

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abstract = "In this note, we introduce and investigate the notion of (Formula presented.) monomial ideals. We give an explicit relation of the (Formula presented.) property to a monomial ideal and its polarization. Further, we characterize the (Formula presented.) property of the ordinary as well as the symbolic third or more powers of squarefree monomial ideals.",

keywords = "CM simplicial complex, Cohen–Macaulay ring, Cohen–Macaulay simplicial complex, generalized Cohen–Macaulay ring, generalized Cohen–Macaulay simplicial complex, simplicial complex",

author = "Pournaki, {M. R.} and K. Shibata and N. Terai and S. Yassemi",

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AU - Pournaki, M. R.

AU - Shibata, K.

AU - Terai, N.

AU - Yassemi, S.

PY - 2022

Y1 - 2022

N2 - In this note, we introduce and investigate the notion of (Formula presented.) monomial ideals. We give an explicit relation of the (Formula presented.) property to a monomial ideal and its polarization. Further, we characterize the (Formula presented.) property of the ordinary as well as the symbolic third or more powers of squarefree monomial ideals.

AB - In this note, we introduce and investigate the notion of (Formula presented.) monomial ideals. We give an explicit relation of the (Formula presented.) property to a monomial ideal and its polarization. Further, we characterize the (Formula presented.) property of the ordinary as well as the symbolic third or more powers of squarefree monomial ideals.

KW - CM simplicial complex

KW - Cohen–Macaulay ring

KW - Cohen–Macaulay simplicial complex

KW - generalized Cohen–Macaulay ring

KW - generalized Cohen–Macaulay simplicial complex

KW - simplicial complex

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JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -

A note on monomial ideals which are Cohen–Macaulay in a fixed codimension

Abstract

Keywords

ASJC Scopus subject areas

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