相关论文: On the ideal $(v^0)$

With each of the usual tree forcings I (e.g., I = Sacks forcing S, Laver forcing L, Miller forcing M, Mathias forcing R, etc.) we associate a sigma--ideal i^0 on the reals as follows: A \in i^0 iff for all T \in I there is S \leq T (i.e. S…

We consider ideals $d^0(\mathcal{V})$ which are generalizations of the ideal $(v^0)$. We formulate couterparts of Hadamard's theorem. Then, adopting the base tree theorem and applying Kulpa-Szyma\'nski Theorem, we obtain $…

Let $G$ be a finite group. Let $K/k$ be a Galois extension of number fields with Galois group isomorphic to $G$, and let $C \subseteq \mathrm{Gal}(K/k) \simeq G$ be a conjugacy invariant subset. It is well known that there exists an…

The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity / minimum rank of the family of symmetric matrices described by G. It is shown that for a…

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 null ideal of the…

Let l^0 and m^0 be the ideals associated with Laver and Miller forcing, respectively. We show that add (l^0) < cov(l^0) and add (m^0) < cov(m^0) are consistent. We also show that both Laver and Miller forcing collapse the continuum to a…

We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\~ between the family of graded lattice ideals in an N-graded polynomial ring over a field K and the family of graded lattice ideals…

The aim of this paper is to give natural examples of $\mathbf{\Sigma}_1^1$-complete and $\mathbf{\Pi}_1^1$-complete sets. In the first part, we consider ideals on $\omega$. In particular, we show that the Hindman ideal $\mathcal{H}$ is…

Let $\Gamma$ be the unit circle, $A(\Gamma)$ the Wiener algebra of continuous functions whose series of Fourier coefficients are absolutely convergent, and $A^+$ the subalgebra of $A(\Gamma)$ of functions whose negative coefficients are…

Let $\fa$ be an ideal of a local ring $(R,\fm)$ and $X$ a $d$-dimensional homologically bounded complex of $R$-modules whose all homology modules are finitely generated. We show that $H^d_{\fa}(X)=0$ if and only if $\dim \hat{R}/\fa…

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…

We say a completely positive contractive map between two C*-algebras has order zero, if it sends orthogonal elements to orthogonal elements. We prove a structure theorem for such maps. As a consequence, order zero maps are in one-to-one…

Let $B$ be an affine Cohen-Macaulay algebra over a field of characteristic $p$. For every prime ideal $\mathfrak{p}\subset B$, let $\text{H}_\mathfrak{p}$ denote $H^{\dim B_\mathfrak{p}}_{\mathfrak{p} B_\mathfrak{p}}\left(…

We work in the Baire space $\mathbb{Z}^\omega$ equipped with the coordinate-wise addition $+$. Consider a $\sigma-$ideal $\mathcal{I}$ and a family $\mathbb{T}$ of some kind of perfect trees. We are interested in results of the form: for…

Wiebe's criterion, which recognizes complete intersections of dimension zero among the class of noetherian local rings, is revisited and exploited in order to provide information on what we call C.I.0-ideals (those such that the…

We study the relationship between the sigma-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category.…

Let $S$ be a semigroup with $0$ and $R$ be a ring with $1$. We extend the definition of the zero-divisor graphs of commutative semigroups to not necessarily commutative semigroups. We define an annihilating-ideal graph of a ring as a…

Let $(G, \Lambda)$ be a self-similar $k$-graph with a possibly infinite vertex set $\Lambda^0$. We associate a universal C*-algebra $\mathcal{O}_{G,\Lambda}$ to $(G,\Lambda)$. The main purpose of this paper is to investigate the ideal…

Let I be a sigma-ideal sigma-generated by a projective collection of closed sets. The forcing with I-positive Borel sets is proper and adds a single real r of an almost minimal degree: if s is a real in V[r] then s is Cohen generic over V…

For any simple graph $G$ on $n$ vertices, the (positive semi-definite) minimum rank of $G$ is defined to be the smallest possible rank among all (positive semi-definite) real symmetric $n\times n$ matrices whose entry in position $(i,j)$,…