Classes of Sequentially Cohen-Macaulay Squarefree Monomial Ideals
نویسندگان
چکیده
منابع مشابه
Sequentially Cohen-macaulay Monomial Ideals of Embedding Dimension Four
Let I be a monomial ideal of the polynomial ring S = K[x1, . . . , x4] over a field K. Then S/I is sequentially Cohen-Macaulay if and only if S/I is pretty clean. In particular, if S/I is sequentially Cohen-Macaulay then I is a Stanley ideal.
متن کاملSequentially Cohen-macaulay Edge Ideals
Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...
متن کاملIntegral Closures of Cohen-macaulay Monomial Ideals
The purpose of this paper is to present a family of CohenMacaulay monomial ideals such that their integral closures have embedded components and hence are not Cohen-Macaulay.
متن کاملTopological Cohen–Macaulay criteria for monomial ideals
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen–Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial ideals. It is unclear whether researchers thinking about this topic have, to this point, been aware of the full spectrum of related developments. Therefore,...
متن کاملCombinatorial Characterizations of Generalized Cohen-macaulay Monomial Ideals
We give a generalization of Hochster’s formula for local cohomologies of square-free monomial ideals to monomial ideals, which are not necessarily square-free. Using this formula, we give combinatorial characterizations of generalized Cohen-Macaulay monomial ideals. We also give other applications of the generalized Hochster’s formula.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2014
ISSN: 1005-3867,0219-1733
DOI: 10.1142/s1005386714000522