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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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.

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

First available in Project Euclid: 5 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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