マツオカ　ナオユキ   MATSUOKA Naoyuki   松岡　直之    所属   明治大学  理工学部    職種   専任教授
言語種別	英語
発行・発表の年月	2016/06
形態種別	学術雑誌
査読	査読あり
標題	Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes
執筆形態	共著(その他)
掲載誌名	Journal of Algebra
掲載区分	国外
巻・号・頁	455,pp.14-31
著者・共著者	Naoyuki Matsuoka, Satoshi Murai
概要	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 almostGorenstein* 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.
DOI	10.1016/j.jalgebra.2016.02.005
ISSN	00218693
PermalinkURL	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84963836263&origin=inward