A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension

M. R. Pournaki, M. Poursoltani, N. Terai, S. Yassemi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
JournalActa Mathematica Vietnamica
Publication statusAccepted/In press - 2021


  • Buchsbaum ring
  • Buchsbaum simplicial complex
  • CM simplicial complex
  • Cohen–Macaulay ring
  • Cohen–Macaulay simplicial complex
  • Simplicial complex

ASJC Scopus subject areas

  • Mathematics(all)


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