相关论文: On the ideal $(v^0)$

In this paper, we prove that for Noetherian graded families $\mathcal{I} = \{I_k\}_{k \ge 0}$ of homogeneous ideals, $\lim\limits_{k \to \infty} \frac{\mathrm{v}(I_k)}{k}$ exists, %equals $\lim\limits_{k \to \infty} \frac{\alpha(I_k)}{k}$,…

Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…

A notion of partial ideal for an operator algebra is a weakening the notion of ideal where the defining algebraic conditions are enforced only in the commutative subalgebras. We show that, in a von Neumann algebra, the ultraweakly closed…

When $G$ is abelian and $l$ is a prime we show how elements of the relative K-group $K_{0}({\bf Z}_{l}[G], {\bf Q}_{l})$ give rise to annihilator/Fitting ideal relations of certain associated ${\bf Z}[G]$-modules. Examples of this…

It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…

Let $R$ be a finite commutative ring with identity, and let $P$ be a proper prime ideal of $R$. The prime ideal graph $\Gamma_P(R)$ has vertex set of $R\setminus\{0\}$, where two distinct vertices $x$ and $y$ are adjacent if and only if…

Let $H$ be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a description of a possible row-factorization $(\RF)$ matrix for each pseudo-Frobenius element of $H.$ Further, when $H$ is symmetric and has…

We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral…

We study zero divisors and minimal prime ideals in semirings of characteristic one. Thereafter we find a counterexample to the most obvious version of primary decomposition, but are able to establish a weaker version. Lastly, we study…

All spaces are assumed to be separable and metrizable. We give a complete classification of the zero-dimensional homogeneous spaces, under the Axiom of Determinacy. This classification is expressed in terms of topological complexity (in the…

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…

We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in [1], in terms of Igusa functions. As corollaries we obtain information about…

We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the…

A family $\mathscr{I} \subseteq [\omega]^\omega$ such that for all finite $\{X_i\}_{i\in n}\subseteq \mathcal I$ and $A \in \mathscr{I} \setminus \{X_i\}_{i\in n}$, the set $A \setminus \bigcup_{i < n} X_i$ is infinite, is said to be ideal…

For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if…

In this dissertation, we tackle the problem of describing the equations of the Rees algebra of I for I =(J,y), with J being of linear type. Throughout, such ideals are referred to as ideals of almost-linear type. In Theorem A, we give a…

For each countable ordinal $\alpha$, we introduce an ideal $conv_\alpha$ and use it to characterize the class of all compact countable spaces which are homeomorphic to the space $\omega^{\alpha}\cdot n+1$ with the order topology. The…

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…

The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…

We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that…