相关论文: On Cebotarev sets

In this note, we present a characterization of sets definable in Skolem arithmetic, i.e., the first-order theory of natural numbers with multiplication. This characterization allows us to prove the decidability of the theory. The idea is…

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist.

The theorem presented in this paper allows the creation of large prime numbers (of order up to o(n^2)) given a table of all primes up to n.

After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…

In this paper we study the set of prime ideals in vector lattices and how the properties of the prime ideals structure the vector lattice in question. The different properties that will be considered are firstly, that all or none of the…

In this paper, we will define $\mathcal{I}^{*}$-sequential topology on a topological space $(X,\tau)$ where $\mathcal{I}$ is an ideal of the subset of natural numbers $\mathbb{N}$. Besides the basic properties of the…

In this paper, we extend a result of Eisenbud-Reeves-Totaro in the frame of ideals of Borel type.

In this paper, we introduce the notion of binomial edge ideals of a clutter and obtain results similar to those obtained for graphs by Rauf \& Rinaldo in \cite{raufrin}. We also answer a question posed in their paper.

We discuss a sufficient condition for a space to be filled with an arbitrary finite number of self-similar spaces using a topological concept.

We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic irreducible integral defining polynomial for each field $K$,…

In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which…

We denote the number of distinct topologies which can be defined on a set $X$ with $n$ elements by $T(n)$. Similarly, $T_0(n)$ denotes the number of distinct $T_0$ topologies on the set $X$. In the present paper, we prove that for any prime…

A classification up to automorphism of the inner ideals of the real finite-dimensional simple Lie algebras is given, jointly with precise descriptions in the case of the exceptional Lie algebras.

We determine the ideal structure of the Toeplitz C*-algebra on the bidisk.

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.

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…

Let $k$ be a number field, $f(x)\in k[x]$ a polynomial over $k$ with $f(0)\neq 0$, and $\O_{k,S}^*$ the group of $S$-units of $k$, where $S$ is an appropriate finite set of places of $k$. In this note, we prove that outside of some natural…

Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them…