Related papers: Spectral hyperspaces of Krasner hyperrings
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.
In this paper, the notions of integral closure of hyperrings and hyperideals in a Krasner hyperring $(R, +, \cdot)$ are defined and some basics properties of them are studied. We define also the notion of hypervaluation hyperideals and then…
In this study, we examine some properties of $r$-hyperideals in the commutative Krasner hyperrings. Some properties of $pr$-hyperideals are also studied. The relation between prime hyperideals and $r$-hyperideals is investigated. We show…
In this article, we will study prime spectrum of Krasner hyperrings and Zariski topology on them, which play an important role in algebraic geometry. Then some results about the relationship between the topological properties of Spec(R) and…
In this paper, we introduce and study the notion of $n$-ary S-hyperideals in a Krasner $(m,n)$-hyperring
We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of this space and detect the spectrality of some of them.
In this paper we aim to introduce some hyperideals such as q-primary, (k,n)-absorbing q-primary, sq-primary, wsq-primary hyperideals.
The aim of this research work is to define and characterize a new class of hyperideals in a Krasner (m,n)-hyperring that we call n-ary J-hyperideals. Also, we study the concept of n-ary delta-J-hyperideals as an expansion of n-ary…
Various classes of hyperideals have been studied in many papers in order to let us fully understand the structures of hyperrings in general. The purpose of this paper is the study of some hyperideals whose concept is created on the basis of…
Let R be a Krasner (m,n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. Several properties and…
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…
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
In this paper, we define the concepts of r-hyperideal and n-hyperideal of the multiplicative hyperring R which are two new classes of hyperideals. Several properties of them are provided.
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
The notions of spectral measures and spectral classes, which are well known for graphs, are generalized and investigated for oriented hypergraphs.
In this paper, our purpose is to introduce and study the notion of weakly n-ary S-primary hyperideals in a commutative Krasner (m,n)-hyperring.
The concern of this paper is to show that there always exist Krasner hyperfields of order n, where n is an integer greater than or equal to 2.
The notion of multiplicative hyperrings is an important class of the algebraic hyper-structures.
The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (theorems 1-4) about the…