Related papers: A generalization of the density zero ideal
One of the main obstacle to study compactness in topological spaces via ideals was the definition of ideal convergence of subsequences as in the existing literature according to which subsequence of an ideal convergent sequence may fail to…
Let (A,p_l)_{l\in\Bbb N} be a Frechet algebra. In this paper, we introduce the concept of Segal Frechet algebra and investigate known results about abstract Segal algebras, for Segal Frechet algebras. Also we recall the concept of…
We prove that measurable sets $E\subset \mathbb R^n$ with locally finite perimeter and zero $s$-mean curvature satisfy the surface density estimates: \begin{align*} \operatorname{Per} (E; B_R(x)) \geq CR^{n-1} \end{align*} for all $R>0$,…
A numerical set is a co-finite subset of the natural numbers that contains zero. Its Frobenius number is the largest number in its complement. Each numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$, which has the…
\textit{Let $E$ be an infinite set on which a property $(\bf P)$ is defined. Suppose that $E=\cup_{i\in I} E_i$ is a partition, where each $E_i$ is infinite. Suppose also that, in each $E_i$, the number of elements satisfying $(\bf P)$ is…
Let $S = \{p_1,\dots,p_r\}$ be a finite set of distinct primes, let $\Psi_S(X)$ be the number of $S$-smooth integers not exceeding $X$, and let $F_S(X)$ be the maximum size of a subset of $M(S) \cap [1,X]$ containing no set $\{n,p_1…
We generalize results of Alladi, Dawsey, and Sweeting and Woo for Chebotarev densities to general densities of sets of primes. We show that if $K$ is a number field and $S$ is any set of prime ideals with natural density $\delta(S)$ within…
Let F denote either the real or complex field. An ideal I in the free *-algebra F<x,x*> in g freely noncommuting variables and their formal adjoints is a *-ideal if I = I*. When a real *-ideal has finite codimension, it satisfies a strong…
In this paper, we study a positive characteristic analogue of the centers of log canonicity of a pair $(R, \Delta)$. We call these analogues centers of $F$-purity. We prove positive characteristic analogues of subadjunction-like results,…
The class of nil-essential ideals is a generalisation of the class of essential ideals. Every nil-essential ideal of a reduced ring is essential. Therefore the intersection of all nil-essential ideals over a reduced ring $R$ is the socle of…
Suppose that $\langle f_n \rangle$ is a sequence of polynomials, $\langle f_n^{(k)}(0)\rangle$ converges for every non-negative integer $k$, and that the limit is not $0$ for some $k$. It is shown that if all the zeros of $f_1, f_2, \dots$…
In recent works by L. Drewnowski and I. Labuda and J. Mart\'inez et al., non-pathological analytic \( P \)-ideals and non-pathological \( F_\sigma \)-ideals have been characterized and studied in terms of their representations by a sequence…
The main result of this paper is an improvement of the upper bound on the cardinal invariant ${\mathord{\mathrm{cov}}}^{\ast}({\mathcal{Z}}_{0})$ that was discovered by Raghavan and Shelah in an earlier paper. Here ${\mathcal{Z}}_{0}$ is…
Suppose that $A \subset \mathbb{R}$ has positive upper density, \[ \limsup_{|I| \to \infty} \frac{|A \cap I|}{|I|} = \delta > 0,\] and $P(t) \in \mathbb{R}[t]$ is a polynomial with no constant or linear term, or more generally a non-flat…
A square-free monomial ideal $I$ is called an {\it $f$-ideal}, if both $\delta_{\mathcal{F}}(I)$ and $\delta_{\mathcal{N}}(I)$ have the same $f$-vector, where $\delta_{\mathcal{F}}(I)$ ($\delta_{\mathcal{N}}(I)$, respectively) is the facet…
We provide an explicit description of the primitive ideals of the enveloping algebra $\operatorname{U}(\frak{sl}(\infty))$ of the infinite-dimensional finitary Lie algebra $\frak{sl}(\infty)$ over an uncountable algebraically closed field…
An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. We concentrate our attention on the separation axioms…
The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…
This is a continuation of the paper [J. Symb. Log. 87 (2022), 1065--1092]. For an ideal $\mathcal{I}$ on $\omega$ we denote $\mathcal{D}_{\mathcal{I}}=\{f\in\omega^\omega: f^{-1}[\{n\}]\in\mathcal{I} \text{ for every $n\in \omega$}\}$ and…
The present paper deals with the asymptotic behavior of equi-coercive sequences $\{\mathcal{F}_n\}$ of nonlinear functionals defined over vector-valued functions in $W_)^{1,p}(\Omega)^M$ , where $p>1$, $M\ge1$, and $\Omega$ is a bounded…