Related papers: Primitive hyperideals and hyperstructure spaces of…
A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this…
We define a superspace over a ring $R$ as a functor on a subcategory of the category of supercommutative $R$-algebras. As an application the notion of a $p$-adic superspace is introduced and used to give a transparent construction of the…
In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts,…
Recently, the Mac\'ias topology has been generalized over integral domains that are not fields, to furnish a topological proof of the infinitude of prime elements under the assumption that the set of units is finite or not open. In this…
The relation space of a hyperplane arrangement is the vector space of all linear dependencies among the defining forms of the hyperplanes in the arrangement. In this paper, we study the relationship between the relation space and the…
We study the topological spectrum of a seminormed ring $R$ which we define as the space of prime ideals $\mathfrak{p}$ such that $\mathfrak{p}$ equals the kernel of some bounded power-multiplicative seminorm. For any seminormed ring $R$ we…
For a semigroup S of Markov operators on a space of continuous functions, we use S-invariant ideals to describe qualitative properties of S such as mean ergodicity and the structure of its fixed space. For this purpose we focus on primitive…
We classify open maximal subalgebras of all infinite-dimensional linearly compact simple Lie superalgebras. This is applied to the classification of infinite-dimensional Lie superalgebras of vector fields, acting transitively and…
We discuss the appearance of Jacobi automorphic forms in the theory of superconformal vertex algebras, explaining it by way of supercurves and formal geometry. We touch on related topics such as Ramanujan's differential equations for…
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…
The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures…
We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the…
In this paper we introduce primigraph spaces, which are topological spaces together with a sheaf of $C^*$-algebras that can be covered by some Prim A's, that is, by the primitive spectra of some $C^*$-algebras endowed with Jacobson topology…
The aim of this paper is to study some distinguished classes of $k$-ideals of semirings, which include $k$-prime, $k$-semiprime, $k$-radical, $k$-irreducible, and $k$-strongly irreducible ideals. We discuss some of the properties of…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every…
We give an explicit description of cubic rings over a discrete valuation ring, as well as a description of all ideals of such rings.
We interpret a valuation $v$ on a ring $R$ as a map $v: R \to M$ into a so called bipotent semiring $M$ (the usual max-plus setting), and then define a \textbf{supervaluation} $\phi$ as a suitable map into a supertropical semiring $U$ with…
In this article we introduce the study of fuzzy semihyperrings and fuzzy R-semihypermodules, where R is a semihyperrings and R-semihypermodules are represntations of R. In particular, semihyperrings all of whose hyperideals are idempotent,…
By a characterization of semiprime $SA$-rings by Birkenmeier, Ghirati and Taherifar in \cite[Theorem 4.4]{B}, and by the topological characterization of $C(X)$ as a Baer-ring by Stone and Nakano in \cite[Theorem 3.25]{KM}, it is easy to see…