Related papers: Spectrality and monoids
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.
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.
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.
We describe which topological spaces can arise as the prime spectrum of a commutative monoid, in the spirit of Hochster's and Brenner's theses.
We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…
Using a new definition of a prime ideal of a skew brace A, on set Spec A of prime ideals of A we endow a spectral topology (in the sense of Grothendieck). We characterize irreducible closed subsets of Spec A and prove every irreducible…
We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil…
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
A bounded set $\Omega \subset \mathbb{R}^d$ is called a spectral set if the space $L^2(\Omega)$ admits a complete orthogonal system of exponential functions. We prove that a cylindric set $\Omega$ is spectral if and only if its base is a…
In this paper we define a topology with sufficiently good properties on the set of prime ideals of a number field.
A "spectral convex set" is a collection of symmetric matrices whose range of eigenvalues form a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal-Sottile-Sturmfels (2011). We study this class…
A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X, closed under finite intersections.…
Let $A$ be a polytope in $\mathbb{R}^d$ (not necessarily convex or connected). We say that $A$ is spectral if the space $L^2(A)$ has an orthogonal basis consisting of exponential functions. A result due to Kolountzakis and Papadimitrakis…
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…
Pursuing ideas of Jeff Smith, we develop a homotopy theory of ideals of monoids in a symmetric monoidal model category. This includes Smith ideals of structured ring spectra and of differential graded algebras. Such Smith ideals are NOT…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
Solenoids are inverse limit spaces over regular covering maps of closed manifolds. M.C. McCord has shown that solenoids are topologically homogeneous and that they are principal bundles with a profinite structure group. We show that if a…
We show that the monoidal product on the stable homotopy category of spectra is essentially unique. This strengthens work of this author with Schwede on the uniqueness of models of the stable homotopy theory of spectra. As an application we…
We prove that the space of radical ideals of a ring $R$, endowed with the hull-kernel topology, is a spectral space, and that it is canonically homeomorphic to the space of the nonempty Zariski closed subspaces of Spec$(R)$, endowed with a…
In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…