Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes

Naoyuki Matsuoka, Satoshi Murai

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we study simplicial complexes whose Stanley-Reisner rings are almost Gorenstein and have a-invariant zero. We call such a simplicial complex an almost Gorenstein* simplicial complex. To study the almost Gorenstein* property, we introduce a new class of simplicial complexes which we call uniformly Cohen-Macaulay simplicial complexes. A d-dimensional simplicial complex δ is said to be uniformly Cohen-Macaulay if it is Cohen-Macaulay and, for any facet F of δ, the simplicial complex δ\ (F) is Cohen-Macaulay of dimension d. We investigate fundamental algebraic, combinatorial and topological properties of these simplicial complexes, and show that almost Gorenstein* simplicial complexes must be uniformly Cohen-Macaulay. By using this fact, we show that every almost Gorenstein* simplicial complex can be decomposed into those of having one dimensional top homology. Also, we give a combinatorial criterion of the almost Gorenstein* property for simplicial complexes of dimension ≤2.

Original languageEnglish
Pages (from-to)14-31
Number of pages18
JournalJournal of Algebra
Volume455
DOIs
Publication statusPublished - 2016 Jun 1
Externally publishedYes

Keywords

  • Almost Gorenstein rings
  • Doubly Cohen-Macaulay rings
  • Stanley-Reisner rings

ASJC Scopus subject areas

  • Algebra and Number Theory

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