Related papers: On spectral types of semialgebraic sets

Let $R$ be a commutative noetherian ring, and $\mathcal{Z}$ a stable under specialization subset of $\Spec(R)$. We introduce a notion of $\mathcal{Z}$-cofiniteness and study its main properties. In the case $\dim(\mathcal{Z})\leq 1$, or…

In this paper, we study meromorphic functions on a domain $\Omega \subset \mathbb{C}$ whose image has finite spherical area, counted with multiplicity. The paper is composed of two parts. In the first part, we show that the limit of a…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

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…

Let $S$ be an additively idempotent semiring and $\mathbf{M}_n(S)$ be the semiring of all $n\times n$ matrices over $S$. We characterize the conditions of when the semiring $\mathbf{M}_n(S)$ is congruence-simple provided that the semiring…

Inspired by the construction of the Cuntz semigroup for a C*-algebra, we introduce the matrix Malcolmson semigroup and the finitely presented module Malcolmson semigroup for a unital ring. These two semigroups are shown to have isomorphic…

Given any arbitrary semi-algebraic set $X$, any two points in $X$ may be joined by a piecewise $C^2$ path $\gamma$ of shortest length. Suppose $\mathcal{A}$ is a semi-algebraic stratification of $X$ such that each component of $\gamma \cap…

Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and…

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology.…

T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

This paper studies Hamiltonian circle actions, i.e. circle subgroups of the group Ham(M,\om) of Hamiltonian symplectomorphisms of a closed symplectic manifold (M,\om). Our main tool is the Seidel representation of \pi_1(\Ham(M,\om)) in the…

Let S and R be the rings of regular functions on affine algebraic varieties over a field of characteristic 0, R be embedded as a subring in S, and F : S --> S be an endomorphism such that F(R) subset R. Suppose that every ideal of height 1…

We show that if a compact, connected, and oriented $n$-manifold $M$ without boundary admits a non-constant non-injective uniformly quasiregular self-map, then the dimension of the real singular cohomology ring $H^*(M; \mathbb{R})$ of $M$ is…

In the additive topological group $(\mathbb{R},+)$ of real numbers, we construct families of sets for which elements are not measurable in the Lebesgue sense. The constructed families have algebraic structures of being semigroups (i.e.,…

We prove that the centralizer Cen(f) in Hom_R(M,M) of a nilpotent endomorphism f of a finitely generated semisimple left R-module M (over an arbitrary ring R) is the homomorphic image of the opposite of a certain Z(R)-subalgebra of the full…

Let $M$ be a non-zero module over an associative (not necessarily commutative) ring. In this paper, we investigate the so-called \emph{second} and \emph{coprime} submodules of $M.$ Moreover, we topologize the spectrum $%…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

For any ring $R$, we introduce an invariant in the form of a partially ordered abelian semigroup $\mathrm{S}(R)$ built from an equivalence relation on the class of countably generated projective modules. We call $\mathrm{S}(R)$ the Cuntz…

Let $\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\mathcal E$ (which means that $\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all…