Related papers: A short note on containment of cores

We prove a number of results involving the kernel of the identity minus the monodromy on the vanishing cycles.

Based on the Thomas-Fermi approach, we describe and distinguish the electron distributions around extended nuclear cores: (i) in the case that cores are neutral for electrons bound by protons inside cores and proton and electron numbers are…

Given an ideal $\mathcal{I}$ on $\omega$ and a sequence $x$ in a topological vector space, we let the $\mathcal{I}$-core of $x$ be the least closed convex set containing $\{x_n: n \notin I\}$ for all $I \in \mathcal{I}$. We show two…

Simulations of idealised star-forming filaments of finite length typically show core growth which is dominated by two cores forming at its respective end. The end cores form due to a strong increasing acceleration at the filament ends which…

D. Rees and J. Sally defined the core of an $R$-ideal $I$ as the intersection of all $($minimal$)$ reductions of $I$. However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently,…

We address a problem posed in [1] by demonstrating through an example that, in the absence of separability, the property of sequential cone compactness does not generally imply cone compactness.

Reason for withdrawal: There is a serious mistake in the calculation of the divisor of the rational section used in the proof of Prop. 2.2.1., and with the correct value the argument does not work.

We prove cancellation theorems for special ideals in Gorenstein local rings. These theorems take the form that if KI is contained in JI, then K is contained in J.

The purpose of this paper is to present a family of Cohen-Macaulay monomial ideals such that their integral closures have embedded components and hence are not Cohen-Macaulay.

In this article, we show that the $N$-center problem with rational weak and moderate forces is not rationally integrable for all but a finite number of values $\alpha\in(0,2)\cap \mathbb{Q}$, where $\alpha$ is the order of the…

We show that in general the third symbolic power of a radical ideal of points in the complex projective plane is not contained in the second usual power of that ideal. This answers in negative a question asked by Huneke and generalized by…

We give a complete classification of the ideals of the core of the C*-algebras associated with self-similar maps under a certain condition. Any ideal is completely determined by the intersection with the coefficient algebra C(K) of the…

Let $R$ be a local Gorenstein ring with infinite residue field of arbitrary characteristic. Let $I$ be an $R$--ideal with $g=\height I >0$, analytic spread $\ell$, and let $J$ be a minimal reduction of $I$. We further assume that $I$…

We begin a discussion about the maximal containments of lower central series ideals: ideals generated by products of two-sided ideals of the lower central series of the free associative algebra on $n$ generators. We introduce two new ideas…

The core of an ideal is the intersection of all its reductions. For large classes of ideals I we explicitly describe the core as a colon ideal of a power of a single reduction and a power of I.

When evaluating the lengthy inclusion-exclusion expansion many of its terms may turn out to be zero, and hence should be discarded beforehand. Often this can be done. The main idea is that the index sets of nonzero terms constitute a set…

Without any restrictions on the base field, we compute the hull and prove a conjecture of Eisenbud and Sturmfels giving an unmixed decomposition of a cellular binomial ideal. Over an algebraically closed field, we further obtain an explicit…

The purpose of this note is to show a new series of examples of homogeneous ideals $I$ in ${\mathbb K}[x,y,z,w]$ for which the containment $I^{(3)}\subset I^2$ fails. These ideals are supported on certain arrangements of lines in ${\mathbb…

We show that the experimental evidence presented in this paper is insufficient to support its conclusions.

In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds.