Related papers: Some arithmetic properties of matroidal ideals
We introduce the Macaulay2 package HomologicalShiftIdeals. It allows to compute the homological shift ideals of a monomial ideal, and to check the homological shift properties, including having linear resolution, having linear quotients, or…
It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…
We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.
We present in this paper a routine which construct the ideal generated by a list of elements in a matrix Lie algebra at any particular characteristic. We have used this algorithm to analyze the problem of the simplicity of some Lie…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers are investigated.
In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters…
Subject to hypotheses based on the matroid structure theory of Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the class of golden-mean matroids and several other closely related classes of…
We introduce the notion of Q-Borel ideals: ideals which are closed under the Borel moves arising from a poset Q. We study decompositions and homological properties of these ideals, and offer evidence that they interpolate between Borel…
Let $R$ be a commutative ring with a collection of ideals $\{ N_1, N_2, \dots, N_{k-1}\}$ satisfying certain conditions, properties of the set of invertible quadratic residues of the ring $R$ are described in terms of properties of the set…
In this paper, we investigate the arithmetical rank of a binomial ideal $J$. We provide lower bounds for the binomial arithmetical rank and the $J$-complete arithmetical rank of $J$. Special attention is paid to the case where $J$ is the…
This paper gives exact formulas for the regularity of edge ideals of edge-weighted integrally closed trees. In addition, we provide some linear upper bounds on the regularity of powers of such ideals.
This paper collects many results on galoisian ideals and Galois theory.
We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that for fixed rank their Ehrhart polynomials are computable in polynomial…
Let $A$ be a unitary ring and let $(\mathbf{I(A),\subseteq })$ be the lattice of ideals of the ring $A.$ In this article we will study the property of the lattice $(\mathbf{I(A),\subseteq})$ to be Noetherian or not, for various types of…
We discuss several extension properties of matroids and polymatroids and their application as necessary conditions for the existence of different matroid representations, namely linear, folded linear, algebraic, and entropic…
We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.
We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.
We study some properties of graded idealizer rings with an emphasis on applications to the theory of noncommutative projective geometry. In particular we give examples of rings for which the $\chi$-conditions of Artin and Zhang and the…