Related papers: On monomial Golod ideals

We use initially regular sequences that consist of linear sums to explore the depth of $R/I^2$, when $I$ is a monomial ideal in a polynomial ring $R$. We give conditions under which these linear sums form regular or initially regular…

The main focus of this paper is on the problem of relating an ideal $I$ in the polynomial ring $\mathbb Q[x_1, \dots, x_n]$ to a corresponding ideal in $\mathbb F_p[x_1,\dots, x_n]$ where $p$ is a prime number; in other words, the…

We introduce a new class of monomial ideals, called strong Borel type ideals, and we compute the Mumford-Castelnouvo regularity for principal strong Borel type ideals. Also, we describe the d-fixed ideals generated by powers of variables…

We give a positive answer to the Huneke-Wiegand Conjecture for monomial ideals over free numerical semigroup rings, and for two generated monomial ideals over complete intersection numerical semigroup rings.

In this paper we study the concept of radical factorization in the context of abstract ideal theory in order to obtain a unified approach to the theory of factorization into radical ideals and elements in the literature of commutative…

Given a graded ideal $I$ in a polynomial ring over a field $K$ it is well known, that the number of distinct generic initial ideals of $I$ is finite. While it is known that for a given $d\in\N$ there is a global upper bound for the number…

We consider the fiber cone of monomial ideals. It is shown that for monomial ideals $I\subset K[x,y]$ of height $2$, generated by $3$ elements, the fiber cone $F(I)$ of $I$ is a hypersurface ring, and that $F(I)$ has positive depth for…

We characterize the class of ideals of a polynomial ring such that the hilbert series of their graded local cohomology modules is maximal.

Proofs of two results about a monomial ideal -- describing membership in auxiliary ideals associated to the monomial ideal -- are given which do not invoke resolution of singularities. The AM--GM inequality is used as a substitute for…

For a polynomial ring S in n variables, we consider the natural action of the symmetric group S_n on S by permuting the variables. For an S_n-invariant monomial ideal I in S and j >= 0, we give an explicit recipe for computing the modules…

We introduce the combinatorial Lyubeznik resolution of monomial ideals. We prove that this resolution is isomorphic to the usual Lyubezbnik resolution. As an application, we give a combinatorial method to determine if an ideal is a…

A direct proof is presented of a form of Alvise Trevisan's result, that every monomial ideal ring is represented by the cohomology of topological space. Certain of these rings are shown to be realized by polyhedral products indexed by…

We introduce the concept of quasi-linearity and prove it is necessary for a monomial ideal to have a linear resolution and identify all the quasi-linear quadratic monomial ideals. We define a strongly linear monomial for a monomial ideal…

In this note we calculate the multiplier ideal associated to an arbitrary monomial ideal in C^n. We discuss applications to the calculation of log canonical thresholds.

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…

In this paper we investigate the monomial ideals which satisfy the copersistence property or nearly copersistence property.

For any ideal $I$ in a Noetherian local ring or any graded ideal $I$ in a standard graded $K$-algebra over a field $K$, we introduce the socle module $\mathrm{Soc}(I)$, whose graded components give us the socle of the powers of $I$. It is…

Let $R$ be a polynomial ring over a field. We prove an upper bound for the multiplicity of $R/I$ when $I$ is a homogeneous ideal of the form $I=J+(F)$, where $J$ is a Cohen-Macaulay ideal and $F\notin J$. The bound is given in terms of two…

This paper introduces the concept of metric ideals in AL-monoids. We also examine the structure of AL-monoids and describe some of the properties of homomorphism and fundamentalisomorphism theorems.Additionaly we introduce and examine a…

We show that all monomial ideals in the polynomial ring in at most 3 variables are pretty clean and that an arbitrary monomial ideal $I$ is pretty clean if and only if its polarization $I^p$ is clean. This yields a new characterization of…