منابع مشابه
Integral 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 کاملSequentially 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 کامل. A C ] 1 2 A ug 2 00 3 GENERIC COHEN - MACAULAY MONOMIAL IDEALS
Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree compl...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2004
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-004-0204-8