Related papers: Ideals on countable sets: a survey with questions
One point compactification is studied in the light of ideal of subsets of $\mathbb{N}$. $\mathcal{I}$-proper map is introduced and showed that a continuous map can be extended continuously to the one point $\mathcal{I}$-compactification if…
We continue the study of the rich family of norm-closed, automorphism invariant ideals of a continuous nest algebra. First we present a unified framework which captures all stable ideals as the kernels of limits of diagonal compressions. We…
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
Several numerical indices that control the normalization of ideals are introduced and some relationships among them are derived.
Given an ideal $\mathcal{I}$ on the nonnegative integers $\omega$ and a Polish space $X$, let $\mathscr{L}(\mathcal{I})$ be the family of subsets $S\subseteq X$ such that $S$ is the set of $\mathcal{I}$-limit points of some sequence taking…
A set $X \subseteq 2^\omega$ with positive measure contains a perfect subset. We study such perfect subsets from the viewpoint of computability and prove that these sets can have weak computational strength. Then we connect the existence of…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
A family I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal I on X is below an ideal J on Y in the Katetov order if there is a function $f:Y\to X$ such that…
In our earlier article~\cite{CanSakran} we initiated a study of the complement-finite submonoids of the group of integer points of a unipotent linear algebraic group. In the present article, we continue to develop tools and techniques for…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
An ideal $I$ is a family of subsets of positive integers $\textbf{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_n)$ of real numbers is said to be $I$-convergent to a real number $L$, if for each…
The goal of this work is to study the ideals of the Goldman Lie algebra $S$. To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure…
Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit description of a set of…
A cover by left ideals of an associative (not necessarily commutative or unital) ring $R$ is a collection of proper left ideals whose set-theoretic union equals $R$. If such a cover exists, then $\eta_\ell(R)$ is the cardinality of a…
We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
In the set of continuous functions C(X,Y) where Y has a topology close to being discrete, there is an equivalence relation on X which characterizes the quasi-components of X. If Y satisfies weak algebraic conditions with a single binary…
Let R be a commutative ring with identity and N(R) be the set of all nilpotent elements of R. The aim of this paper is to introduce and study the notion of nil-prime ideals as a generalization of prime ideals. We say that a proper ideal P…
We determine the set of catenary degrees, the set of distances, and the unions of sets of lengths of the monoid of nonzero ideals and of the monoid of invertible ideals of orders in quadratic number fields.