Related papers: Differentially fixed ideals in toric varieties
We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.
This paper concerns the exponentiation of monomial ideals. While it is customary for the exponentiation operation on ideals to consider natural powers, we extend this notion to powers where the exponent is a positive real number. Real…
The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see,…
In this article, we define three new operations on ideals which generalize integral closure and Frobenius closure of ideals, whose definitions incorporate an auxiliary ideal and a real parameter. These additional ingredients are common in…
Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
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.
We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also…
Given a $d \times n$ integer matrix $A$, the main result is an elementary, simple-to-state algorithm that finds the largest $A$-graded ideal contained in any ideal $I$ in a polynomial ring $\Bbbk[x_1,\ldots,x_n]$. The special case where $A$…
The ring of periodic distributions on ${\mathbb{R}}^{\tt d}$ with usual addition and with convolution is considered. Via Fourier series expansions, this ring is isomorphic to the ring ${\mathcal{S}}'({\mathbb{Z}}^{\tt d})$ of all maps…
In a recent work, Fouli and Lin generalized a Villarreal's result and showed that if each connected components of the line graph of a squarefree monomial ideal contains at most a unique odd cycle, then this ideal is of linear type. In this…
Given an affine algebraic variety V and a quantization A of its coordinate ring, it is conjectured that the primitive ideal space of A can be expressed as a topological quotient of V. Evidence in favor of this conjecture is discussed, and…
This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article positively answers a question of Avramov for such a ring $R$.…
We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of…
In this article we study thick ideals defined by periodic self maps in the stable motivic homotopy category over $\mathbb{C}$. In addition, we extend some results of Ruth Joachimi about the relation between thick ideals defined by motivic…
In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are…
A notion of partial ideal for an operator algebra is a weakening the notion of ideal where the defining algebraic conditions are enforced only in the commutative subalgebras. We show that, in a von Neumann algebra, the ultraweakly closed…
In this paper, we view the collection of ideals of a commutative principal ideal ring from two perspectives: one as an ordered semigroup I(R) and the other as a category I_R . It is shown that I(R) is a regular ordered semigroup whereas I_R…
In this paper, we discuss the normality of the toric rings of stable set polytopes, and the set of generators and Gr\"obner bases of toric ideals of stable set polytopes by using the results on that of edge polytopes of finite nonsimple…
Normal affine algebraic varieties in characteristic 0 are uniquely determined (up to isomorphism) by the Lie algebra of derivations of their coordinate ring. This is not true without the hypothesis of normality. But, we show that (in…