Journal of Commutative Algebra

SURVEY ARTICLE: Simplicial complexes satisfying Serre's condition: A survey with some new results

M.R. Pournaki, S.A. Seyed Fakhari, N. Terai, and S. Yassemi

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Abstract

The problem of finding a characterization of Cohen--Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen--Macaulay simplicial complexes.

Article information

Source
J. Commut. Algebra, Volume 6, Number 4 (2014), 455-483.

Dates
First available in Project Euclid: 5 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1420466340

Digital Object Identifier
doi:10.1216/JCA-2014-6-4-455

Mathematical Reviews number (MathSciNet)
MR3294858

Zentralblatt MATH identifier
1345.13014

Subjects
Primary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 05E99: None of the above, but in this section
Secondary: 13C13: Other special types

Keywords
Simplicial complex Cohen-Macaulay simplicial complex ($S_r$) simplicial complex sequentially Cohen-Macaulay simplicial complex sequentially ($S_r$) simplicial complex

Citation

Pournaki, M.R.; Fakhari, S.A. Seyed; Terai, N.; Yassemi, S. SURVEY ARTICLE: Simplicial complexes satisfying Serre's condition: A survey with some new results. J. Commut. Algebra 6 (2014), no. 4, 455--483. doi:10.1216/JCA-2014-6-4-455. https://projecteuclid.org/euclid.jca/1420466340


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