Related papers: Distinguished classes of ideal spaces and their to…
Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we intend to show that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.
The aim of this note is to prove that the set of proper normal subgroups of a group endowed with coarse lower topology is a spectral space.
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the…
We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…
As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain topological properties exhibited by distinguished classes of…
The purpose of this paper is to introduce a Zariski-like topology on the spectrum of all proper ideals of a ring. We show that the space is T_0, quasi-compact, and every irreducible closed subset has a unique generic point. Furthermore,…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
In the present survey paper, we present several new classes of Hochster's spectral spaces "occurring in nature", actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The…
Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly…
This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The…
Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…
Consideration of certain properties of group rings and their ideals search
In this paper we have introduced the notion of $\mathcal{I}$-density topology in the space of reals introducing the notions of upper $\mathcal{I}$-density and lower $\mathcal{I}$-density where $\mathcal{I}$ is an ideal of subsets of the set…
The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied.
For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…
In this paper, we introduce round and sleek topological spaces and study their properties.
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…