相关论文: Discrete $z$-filters and rings of analytic functio…

Consider the subring $\mathcal{R}_cL$ of continuous real-valued functions defined on a frame $L$, comprising functions with a countable pointfree image. We present some useful properties of $\mathcal{R}_cL$. We establish that both…

The set of all maximal ideals of the ring $\mathcal{M}(X,\mathcal{A})$ of real valued measurable functions on a measurable space $(X,\mathcal{A})$ equipped with the hull-kernel topology is shown to be homeomorphic to the set $\hat{X}$ of…

In this paper, the concepts of $K$-subset systems and $k$-well-filtered spaces are introduced, which provide another uniform approach to $d$-spaces, $s$-well-filtered spaces (i.e., $\mathcal{U}_{S}$-admissibility) and well-filtered spaces.…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

Consider the ring $C_c(X)_F$ of real valued functions which are discontinuous on a finite set with countable range. We discuss $(\mathcal{Z}_c)_F$-filters on $X$ and $(\mathcal{Z}_c)_F$-ideals of $C_c(X)_F$. We establish an analogous…

Let $ M (X)$ be the ring of all real measurable functions on a measurable space $(X, \mathscr{A})$. In this article, we show that every ideal of $M(X)$ is a $Z^{\circ}$-ideal. Also, we give several characterizations of maximal ideals of…

Let $S$ be an infinite discrete semigroup. The operation on $S$ extends uniquely to the Stone-\v{C}ech compactification $\beta S$ making $\beta S$ a compact right topological semigroup with $S$ contained in its topological center. As such,…

We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces -- including the infinitely many so-called accordion spaces for which filtered K-theory…

The ring of periodic distributions on ${\mathbb{R}}^{\tt d}$ with usual addition and with convolution is considered. Via Fourier series expansions, this ring is isomorphic to the ring ${\mathcal{S}}'({\mathbb{Z}}^{\tt d})$ of all maps…

We introduce the decomposability spectrum $K_D=\{\lambda \geq \omega| D \text{is} \lambda\text{-decomposable}\}$ of an ultrafilter $D$, and show that Shelah's $\pcf$ theory influences the possible values $K_D$ can take. For example, we show…

Let f: X -> Y be a separated morphism of schemes of finite type over a finite field of characteristic p, let Lambda be an artinian local Z_p-algebra with finite residue field, let m be the maximal ideal of Lambda, and let L^\bullet be a…

Let $\Sigma (X,\mathbb{C})$ denote the collection of all the rings between $C^*(X,\mathbb{C})$ and $C(X,\mathbb{C})$. We show that there is a natural correlation between the absolutely convex ideals/ prime ideals/maximal…

Given a compact Polish space $E$ and the hyperspace of its compact subsets $\mathcal{K}(E)$, we consider the class of $G_{\delta}$ $\sigma$-ideals of compact subsets of $E$ that can be represented via a compact subset of $\mathcal{K}(E)$.…

Let $L$ be a nilpotent algebra of class two over a compact discrete valuation ring $A$ of characteristic zero or of sufficiently large positive characteristic. Let $q$ be the residue cardinality of $A$. The ideal zeta function of $L$ is a…

Let K be an expansion of either an ordered field or a valued field. Given a definable set X $\subseteq$ K^m let C(X) be the ring of continuous definable functions from X to K. Under very mild assumptions on the geometry of X and…

Let $PQC$ stand for the set of all piecewise quasicontionus function on the unit circle, i.e., the smallest closed subalgebra of $L^\infty(\mathbb{T})$ which contains the classes of all piecewise continuous function $PC$ and all…

Given a contractive tuple of Hilbert space operators satisfying certain $A$-relations we show that there exists a unique minimal dilation to generators of Cuntz-Krieger algebras or its extension by compact operators. This Cuntz-Krieger…

Our aim is to study certain algebraic properties of the ring $C(X)_\mathcal{P}$ of real-valued functions on $X$ whose closure of discontinuity set is in an ideal of closed sets. We characterize $\mathcal{P}P$-spaces using $z$-ideals and…

Let $\mathcal{Z(R)}$ be the set of zero divisor elements of a commutative ring $R$ with identity and $\mathcal{M}$ be the space of minimal prime ideals of $R$ with Zariski topology. An ideal $I$ of $R$ is called strongly dense ideal or…

The authors establish a connection between the Quillen K-theory of certain local fields and the de Rham-Witt complex of their rings of integers with logarithmic poles at the maximal ideal. They consider fields K that are complete discrete…