相关论文: The Principal Ideal Theorem in Spectral Synthesis

We consider the polynomial ring in finitely many variables over an algebraically closed field of positive characteristic, and initiate the systematic study of ideals preserved by the action of the general linear group by changes of…

In this paper, a spectral theorem is proved for self-adjoint cyclically compact partial integral operators in the space of functions with mixed norm, which is a Kaplansky--Hilbert module. The decomposition through eigenfunctions, integral…

Let $X$ be a completely regular topological space. We assign to each (set theoretic) ideal of $X$ an (algebraic) ideal of $C_B(X)$, the normed algebra of continuous bounded complex valued mappings on $X$ equipped with the supremum norm. We…

We propose a method to unify various stability results about symmetric ideals in polynomial rings by stratifying related derived categories. We execute this idea for chains of $GL_n$-equivariant modules over an infinite field $k$ of…

To each prime ideal in a polynomial ring over a field we associate an algebraic matroid and show that it is preserved under tropicalization. This gives a necessary condition for a tropical variety to be set-theoretically realizable from a…

In this paper we use some results related to regularity, Betti numbers and reduction of generic initial ideals, showing their stability in passing from an ideal to its initial ideal if the last has some simple properties.

We study a notion called $n$-standardness (defined by M. E. Rossi and extended in this paper) of ideals primary to the maximal ideal in a Cohen-Macaulay local ring and some of its consequences. We further study conditions under which the…

In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…

Let $R=\mathbf{C}[\xi_1,\xi_2,\ldots]$ be the infinite variable polynomial ring, equipped with the natural action of the infinite symmetric group $\mathfrak{S}$. We classify the $\mathfrak{S}$-primes of $R$, determine the containments among…

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the…

We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest value of the largest real part of the spectrum of a matrix system.…

We use the notion of $\A$-compact sets, which are determined by a Banach operator ideal $\A$, to show that most classic results of certain approximation properties and several Banach operator ideals can be systematically studied under this…

We identify a regularity property for structured ring spectra, and with it we prove a natural analogue of Quillen's localization theorem for algebraic K-theory in this setting.

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

We study the set of circuits of a homogeneous ideal and that of its truncations, and introduce the notion of generic circuits set. We show how this is a well-defined invariant that can be used, in the case of initial ideals with respect to…

We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…

We prove Suslin's local-global principle for principal congruence subgroups of Chevalley groups. Let $G$ be a Chevalley--Demazure group scheme with a root system $\Phi\ne A_1$ and $E$ its elementary subgroup. Let $R$ be a ring and $I$ an…

The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…

In this paper, we introduce the concept of ideal on CL-algebra. It is proved that this concept generalizes the notion of ideal on Residuated Lattices. Prime ideal on CL-algebra are defined and few interesting properties are obtained. It has…

In this paper we use the Galois module structure for the classical parameterizing spaces for elementary p-abelian extensions of a field K to give necessary and sufficient conditions for the solvability of any embedding problem which is an…