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Survey article: Simplicial complexes satisfying Serre's condition: A survey with some new results
, Article Journal of Commutative Algebra ; Vol. 6, issue. 4 , 2014 , p. 455-483 ; Seyed Fakhari, S. A ; Terai, N ; Yassemi, S ; Sharif University of Technology
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
A note on monomial ideals which are Cohen–Macaulay in a fixed codimension
, Article Communications in Algebra ; Volume 50, Issue 11 , 2022 , Pages 4988-4996 ; 00927872 (ISSN) ; Shibata, K ; Terai, N ; Yassemi, S ; Sharif University of Technology
Taylor and Francis Ltd
2022
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. © 2022 Taylor & Francis Group, LLC
A brief survey on pure cohen–macaulayness in a fixed codimension
, Article Acta Mathematica Vietnamica ; 2021 ; 02514184 (ISSN) ; Poursoltani, M ; Terai, N ; Yassemi, S ; Sharif University of Technology
Springer
2021
Abstract
A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CMt simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CMt simplicial complexes. © 2021, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd
A brief survey on pure cohen–macaulayness in a fixed codimension
, Article Acta Mathematica Vietnamica ; Volume 47, Issue 1 , 2022 , Pages 181-196 ; 02514184 (ISSN) ; Poursoltani, M ; Terai, N ; Yassemi, S ; Sharif University of Technology
Springer
2022
Abstract
A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CMt simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CMt simplicial complexes. © 2021, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd