Related papers: On the Primitive Ideals of Nest Algebras

We give a necessary and sufficient criterion for an operator in a nest algebra to belong to a proper two-sided ideal of that algebra. Using this result, we describe the strong radical of a nest algebra, and give a general description of the…

We classify the primitive ideals of generalized down-up algebras

Given a unital associative ring S and a subring R, we say that S is an ideal (or Dorroh) extension of R if for some ideal I of S, S = R + I, where the sum is direct. In this note we investigate the ideal structure of an arbitrary ideal…

The aim of this paper is to study the primitive ideals of Novikov algebras. In terms of modular maximal right ideals, a characterization of the primitive ideals of a Novikov algebra has been obtained. We prove a Chevalley-Jacobson…

We continue the study of the rich family of norm-closed, automorphism invariant ideals of a continuous nest algebra. First we present a unified framework which captures all stable ideals as the kernels of limits of diagonal compressions. We…

Following the structure theory approach for rings, the aim of this paper is to study some distinguished classes of Lie algebras. We introduce the notion of a Lie-module and discuss some relations of it with various classes of ideals of a…

We introduce a class of left ideals (and subalgebras) of nest algebras determined by totally ordered families of partial isometries on a complex Hilbert space $H$. Let $\mathcal{E}$ be a family of partial isometries that is totally ordered…

We generalize Jacobson's notion of primitive ring to the setting of quantales. We show that every primitive ring gives rise to a primitive quantale of ideals. We then prove a density theorem for strongly primitive quantales. Furthermore, we…

We describe the primitive ideal spaces and the Jacobson topologies of a special class of topological graph algebras.

The paper contributes to the structure theory of primitive axial algebras. For a primitive axial algebra $A$ with a Frobenius form we compare the largest ideal $R(A)$ not containing any of the generating axes, the radical $A^\perp$ of the…

This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primitive elements are found and algorithms are proposed. To prove…

Let N be a nest on a Hilbert space H and AlgN the corresponding nest algebra. We determine the hypocompact radical of AlgN . Other topological radicals are also characterized.

Let $\mathcal G$ be an ultragraph and let $K$ be a field. We describe prime and primitive ideals in the ultragraph Leavitt path algebra $L_K(\mathcal G)$. We identify the graded prime ideals in terms of downward directed sets and then we…

There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the…

In this paper we characterize the maximal modular ideals of an evolution algebra $A\,\ $in order to describe its Jacobson radical, \ $Rad(A).$ We characterize semisimple evolution algebras (i.e. those such that $% Rad(A)=\{0\}$)as well as…

Let $ m , n \in \mathbb{N}$, $D$ be a division ring, and $M_{m \times n}(D)$ denote the bimodule of all $m \times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m \times n}(D)$ in terms of left row…

Consider the Deaconu-Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of the associated groupoid C*-algebra. For a…

We introduce primitive hyperideals of a hyperring R and show relations with R itself, and with maximal and prime hyperideals of R. We endow a Jacobson topology on the set of primitive hyperideals of R and study topological properties of the…

We study symmetric algebras $A$ over an algebraically closed field $F$ in which the Jacobson radical of the center of $A$, the socle of the center of $A$ or the Reynolds ideal of $A$ are ideals.

The purpose of this note is to introduce primitive ideals of noncommutative semigroups and study some topological aspects of the corresponding structure spaces.