Related papers: Some arithmetic properties of matroidal ideals
In this paper, we introduce the concept of complementary edge ideals of graphs and study their algebraic properties and invariants.
The purpose of this note is to give a survey of the algebraic properties of multiplier ideals, and illustrate some of their applications to classical projective geometry.
Although algebraic matroids were discovered in the 1930s, interest in them was largely dormant until their recent use in applications of algebraic geometry. Because nonlinear algebra is computationally challenging, it is easier to work with…
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
All Cohen--Macaulay polymatroidal ideals are classified. The Cohen--Macaulay polymatroidal ideals are precisely the principal ideals, the Veronese ideals, and the squarefree Veronese ideals.
In this thesis, we focus on the study of some classes of monomial ideals, namely lexsegment ideals and monomial ideals with linear quotients.
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
We study when Taylor resolutions of monomial ideals are minimal. We consider monomial ideals with linear quotients. In particular, we determine precisely the stable ideals and the monomial ideals with linear resolutions having the miminal…
Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all…
Taking a ring-theoretic perspective as our motivation, the main aim of this series is to establish a comprehensive theory of ideals in commutative quantales with an identity element. This particular article focuses on an examination of…
In this paper, we aim to introduce and study the notion of Endo-prime hyperideals.
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
We prove the componentwise linearity of ideals that satisfy a certain exchange property similar to polymatroidal ideals. We also discuss the componentwise linearity and exchange properties of ideals of $k$-covers of totally balanced…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
We study the homological shifts of polymatroidal ideals. In our main theorem we prove that the first homological shift ideal of any polymatroidal ideal is again polymatroidal, supporting a conjecture of Bandari, Bayati and Herzog that…
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via techniques from polyhedral geometry. It turns out that the…
We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs.
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
We study some homological properties of the conductor ideal.
The Orlik-Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first we study homological properties of E-modules as e.g. complexity, depth and regularity. In particular, we consider modules with…