We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm ...We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm to compute is given using Macaulay2.For squarefree monomial ideals the problem is related to the combinatorics of the underlying clutter or graph.For ideals of Borel type,the monomial u takes a simpler form,and we classify when is unique.展开更多
Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the prope...Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the property that for all integers 1 ≤ i1 〈 i2 〈 … 〈 it ≤ m such that lcm（uil, ui2,..., uii） = lcm（ul,u2,...,Um）. We give an upper bound for Castelnuovo-Mumford regularity of I by the bigsize of I. As a corollary, the projective dimension of I is bounded by the number w.展开更多
In this paper,we give equivalent conditions for the factor rings of the polynomial ring k[x,y]modulo monomial ideals to be Armendariz rings,where k is a field.For an ideal I with 2 or 3 monomial generators,or n homoge...In this paper,we give equivalent conditions for the factor rings of the polynomial ring k[x,y]modulo monomial ideals to be Armendariz rings,where k is a field.For an ideal I with 2 or 3 monomial generators,or n homogeneous monomial generators,such that k[x,y]/I is an Armendariz ring,we characterize the minimal generator set G(I)of I.展开更多
Let R=K[x1,…,xn]be the polynomial ring in n variables over a field K and I be a matroidal ideal of R.We show that I is sequentially Cohen-Macaulay if and only if the Alexander dual Iy has linear quotients.As a conseq...Let R=K[x1,…,xn]be the polynomial ring in n variables over a field K and I be a matroidal ideal of R.We show that I is sequentially Cohen-Macaulay if and only if the Alexander dual Iy has linear quotients.As a consequence,I is sequentially Cohen-Macaulay if and only if I is shellable.展开更多
Let K be a field and let A = K[X1,...,Xn] be the polynomial ring in X1, ..., Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics c...Let K be a field and let A = K[X1,...,Xn] be the polynomial ring in X1, ..., Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics computing some invariants. Moreover, we study the link between such a special class of squarefree lexsegment ideals and the so-called s-sequences.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 consider the symmetric algebra of a class of monomial ideals generated by s-sequences.For these ideals with linear syzygies,we determine their Jacobian dual modules and study their duality properties.
In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We main...In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We mainly consider the generalization of chordality proposed by Bigdeli et al. in 2017 and the concept of cycles introduced by Can- non and Faridi in 2013, and study their interrelations and algebraic interpretations. In particular, we investigate the relationship between chordality and having linear quotients in some classes of clutters. Also, we show that if e is a clutter such that （ ） is a vertex decomposable simplicial complex or I（ ） is squarefree stable, then is chordal.展开更多
基金Supported by the MATRICS research grant MTR/2018/000420sponsored by the SERB Government of India.
文摘We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm to compute is given using Macaulay2.For squarefree monomial ideals the problem is related to the combinatorics of the underlying clutter or graph.For ideals of Borel type,the monomial u takes a simpler form,and we classify when is unique.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11201326）, the Natural Science Foundation of Jiangsu Province （No. BK2011276）, and the Jiangsu Provincial Training Programs of Innovation and Entrepreneurship for Undergraduates.
文摘Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the property that for all integers 1 ≤ i1 〈 i2 〈 … 〈 it ≤ m such that lcm（uil, ui2,..., uii） = lcm（ul,u2,...,Um）. We give an upper bound for Castelnuovo-Mumford regularity of I by the bigsize of I. As a corollary, the projective dimension of I is bounded by the number w.
文摘In this paper,we give equivalent conditions for the factor rings of the polynomial ring k[x,y]modulo monomial ideals to be Armendariz rings,where k is a field.For an ideal I with 2 or 3 monomial generators,or n homogeneous monomial generators,such that k[x,y]/I is an Armendariz ring,we characterize the minimal generator set G(I)of I.
文摘Let R=K[x1,…,xn]be the polynomial ring in n variables over a field K and I be a matroidal ideal of R.We show that I is sequentially Cohen-Macaulay if and only if the Alexander dual Iy has linear quotients.As a consequence,I is sequentially Cohen-Macaulay if and only if I is shellable.
文摘Let K be a field and let A = K[X1,...,Xn] be the polynomial ring in X1, ..., Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics computing some invariants. Moreover, we study the link between such a special class of squarefree lexsegment ideals and the so-called s-sequences.
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 consider the symmetric algebra of a class of monomial ideals generated by s-sequences.For these ideals with linear syzygies,we determine their Jacobian dual modules and study their duality properties.
文摘In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We mainly consider the generalization of chordality proposed by Bigdeli et al. in 2017 and the concept of cycles introduced by Can- non and Faridi in 2013, and study their interrelations and algebraic interpretations. In particular, we investigate the relationship between chordality and having linear quotients in some classes of clutters. Also, we show that if e is a clutter such that （ ） is a vertex decomposable simplicial complex or I（ ） is squarefree stable, then is chordal.
