The associated primes of an arbitrary lexsegment ideal I C S = K[x1,..., xn] are determined. As application it is shown that S/I is a pretty clean module, therefore S/I is sequentially Cohen-Mazaulay and satisfies Sta...The associated primes of an arbitrary lexsegment ideal I C S = K[x1,..., xn] are determined. As application it is shown that S/I is a pretty clean module, therefore S/I is sequentially Cohen-Mazaulay and satisfies Stanley＇s conjecture.展开更多
We characterize pure lexsegment complexes which are Cohen-Macaulay in arbitrary codimension. More precisely, we prove that any lexsegment complex is Cohen- Macaulay if and only if it is pure and its 1-dimensional link...We characterize pure lexsegment complexes which are Cohen-Macaulay in arbitrary codimension. More precisely, we prove that any lexsegment complex is Cohen- Macaulay if and only if it is pure and its 1-dimensional links are connected, and that a lexsegment flag complex is Cohen-Macaulay if and only if it is pure and connected. We show that any non-Cohen-Macaulay lexsegment complex is a Buchsbaum complex if and only if it is a pure disconnected flag complex. For t≥2, a lexsegment complex is strictly Cohen-Macaulay in codimension t if and only if it is the join of a lexsegment pure discon- nected flag complex with a （t - 2）-dimensional simplex. When the Stanley-Reisner ideal of a pure lexsegment complex is not quadratic, the complex is Cohen-Macaulay if and only if it is Cohen-Macaulay in some codimension. Our results are based on a characterization of Cohen-Macaulay and Buchsbaum lexsegment complexes by Bonanzinga, Sorrenti and Terai.展开更多
In this paper we characterize all the lexsegment ideals which are normally torsion-free. This will provide a large class of normally torsion-free monomial ideals which are not square-free. Our characterization is give...In this paper we characterize all the lexsegment ideals which are normally torsion-free. This will provide a large class of normally torsion-free monomial ideals which are not square-free. Our characterization is given in terms of the ends of the lexsegment. We also prove that, for lexsegment ideals, the property being normally torsion-free is equivalent to the property of the depth function being constant.展开更多
We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen- Macaulay. As an application, we give a complete charac...We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen- Macaulay. As an application, we give a complete characterization of the completely square- free lexsegment ideals which are sequentially Cohen-Macaulay and we also derive formulas for some homological invariants of this class of ideals.展开更多
文摘The associated primes of an arbitrary lexsegment ideal I C S = K[x1,..., xn] are determined. As application it is shown that S/I is a pretty clean module, therefore S/I is sequentially Cohen-Mazaulay and satisfies Stanley＇s conjecture.
文摘We characterize pure lexsegment complexes which are Cohen-Macaulay in arbitrary codimension. More precisely, we prove that any lexsegment complex is Cohen- Macaulay if and only if it is pure and its 1-dimensional links are connected, and that a lexsegment flag complex is Cohen-Macaulay if and only if it is pure and connected. We show that any non-Cohen-Macaulay lexsegment complex is a Buchsbaum complex if and only if it is a pure disconnected flag complex. For t≥2, a lexsegment complex is strictly Cohen-Macaulay in codimension t if and only if it is the join of a lexsegment pure discon- nected flag complex with a （t - 2）-dimensional simplex. When the Stanley-Reisner ideal of a pure lexsegment complex is not quadratic, the complex is Cohen-Macaulay if and only if it is Cohen-Macaulay in some codimension. Our results are based on a characterization of Cohen-Macaulay and Buchsbaum lexsegment complexes by Bonanzinga, Sorrenti and Terai.
文摘In this paper we characterize all the lexsegment ideals which are normally torsion-free. This will provide a large class of normally torsion-free monomial ideals which are not square-free. Our characterization is given in terms of the ends of the lexsegment. We also prove that, for lexsegment ideals, the property being normally torsion-free is equivalent to the property of the depth function being constant.
文摘We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen- Macaulay. As an application, we give a complete characterization of the completely square- free lexsegment ideals which are sequentially Cohen-Macaulay and we also derive formulas for some homological invariants of this class of ideals.
