相关论文: The depth of an ideal with a given Hilbert functio…

An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in…

In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let $I$ be a homogeneous ideal in a polynomial ring over a field of…

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…

There is a longstanding conjecture by Fr\"oberg about the Hilbert series of the ring $R/I$, where $R$ is a polynomial ring, and $I$ an ideal generated by generic forms. We prove this conjecture true in the case when $I$ is generated by a…

For any two integers $d,r \geq 1$, we show that there exists an edge ideal $I(G)$ such that the ${\rm reg}\left(R/I(G)\right)$, the Castelnuovo-Mumford regularity of $R/I(G)$, is $r$, and ${\rm deg} (h_{R/I(G)}(t))$, the degree of the…

Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, then we give precise formulas for values of depth, Stanley depth, projective dimension, regularity and Krull dimension of S/I.

We introduce the notion of G-hypergeometric function, where G is a complex Lie group. In the case when G is a complex torus, this notion amounts to the notion of Gelfand's A-hypergeometric function. We show that the integral $\int…

The structure of the defining ideal of the semigroup ring $k[H]$ of a numerical semigroup $H$ over a field $k$ is described, when the pseudo-Frobenius numbers of $H$ are multiples of a fixed integer.

Consider the ring $\mathcal{S}$ of symmetric polynomials in $k$ variables over an arbitrary base ring $\mathbf{k}$. Fix $k$ scalars $a_{1},a_{2},\ldots,a_{k}\in\mathbf{k}$. Let $I$ be the ideal of $\mathcal{S}$ generated by…

The present paper investigates properties of quasi-stable ideals and of Borel-fixed ideals in a polynomial ring $k[x_0,\dots,x_n]$, in order to design two algorithms: the first one takes as input $n$ and an admissible Hilbert polynomial…

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…

Let $R$ be a polynomial ring over a field $K$. To a given squarefree monomial ideal $I \subset R$, one can associate a hypergraph $H(I)$. In this article, we prove that the arithmetical rank of $I$ is equal to the projective dimension of…

The set of all maximal ideals of the ring $\mathcal{M}(X,\mathcal{A})$ of real valued measurable functions on a measurable space $(X,\mathcal{A})$ equipped with the hull-kernel topology is shown to be homeomorphic to the set $\hat{X}$ of…

In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…

Let $G$ be a finite simple graph and let $I_G$ denote its associated toric ideal in the polynomial ring $R$. For each integer $n\geq 2$, we completely determine all the possible values for the tuple $({\rm reg}(R/I_G), {\rm…

Let $R = k[w, x_1,..., x_n]/I$ be a graded Gorenstein Artin algebra . Then $I = \ann F$ for some $F$ in the divided power algebra $k_{DP}[W, X_1,..., X_n]$. If $RI_2$ is a height one idealgenerated by $n$ quadrics, then $I_2 \subset (w)$…

For a given algebraically closed field $k$ of characteristic $p>0$ we consider the set ${\mathcal C}_k$, of graded isomorphism classes of {\em standard graded pairs} $(R, I)$, where $R$ is a standard graded ring over the field and $I$ is a…

Let $G$ be a graph on the vertex set $[n]$ and $J_G$ the associated binomial edge ideal in the polynomial ring $S=\mathbb{K}[x_1,\ldots,x_n,y_1,\ldots,y_n]$. In this paper we investigate the depth of binomial edge ideals. More precisely, we…

Let $R$ be a polynomial ring in $N$ variables over an arbitrary field $K$ and let $I$ be an ideal of $R$ generated by $n$ polynomials of degree at most 2. We show that there is a bound on the projective dimension of $R/I$ that depends only…

Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{d},y_1,\ldots,y_d]$. We prove that for all $t \ge 1$, $$\operatorname{depth} (S/I^t) = \operatorname{max} \{d -t + 1, 1…